mlpack Julia binding documentation
🔗 mlpack overview
mlpack is an intuitive, fast, and flexible headeronly C++ machine learning library with bindings to other languages. It aims to provide fast, lightweight implementations of both common and cuttingedge machine learning algorithms.
This reference page details mlpack’s bindings to Julia.
Further useful mlpack documentation links are given below.
See also the quickstart guide for Julia:
🔗 Data Formats
mlpack bindings for Julia take and return a restricted set of types, for simplicity. These include primitive types, matrix/vector types, categorical matrix types, and model types. Each type is detailed below.
Int
: An integer (i.e.,1
).Float64
: A floatingpoint number (i.e.,0.5
).Bool
: A boolean flag option (true
orfalse
).String
: A character string (i.e.,"hello"
).Array{Int, 1}
: A vector of integers; i.e.,[0, 1, 2]
.Array{String, 1}
: A vector of strings; i.e.,["hello", "goodbye"]
.Float64 matrixlike
: A 2d matrixlike containingFloat64
data (could be anArray{Float64, 2}
or aDataFrame
or anything convertible to anArray{Float64, 2}
). It is expected that each row of the matrix corresponds to a data point, unlesspoints_are_rows
is set tofalse
when calling mlpack bindings.Int matrixlike
: A 2d matrixlike containingInt
data (elements should be greater than or equal to 0). Could be anArray{Int, 2}
or aDataFrame
or anything convertible to anArray{Int, 2}
. It is expected that each row of the matrix corresponds to a data point, unlesspoints_are_rows
is set tofalse
when calling mlpack bindings.Float64 vectorlike
: A 1d vectorlike containingFloat64
data (could be anArray{Float64, 1}
, anArray{Float64, 2}
with one dimension of size 1, or anything convertible toArray{Float64, 1}
.Int vectorlike
: A 1d vectorlike containingInt
data (elements should be greater than or equal to 0). Could be anArray{Int, 1}
, anArray{Int, 2}
with one dimension of size 1, or anything convertible toArray{Int, 1}
.Tuple{Array{Bool, 1}, Array{Float64, 2}}
: A 2d array containingFloat64
data along with a boolean array indicating which dimensions are categorical (represented bytrue
) and which are numeric (represented byfalse
). The number of elements in the boolean array should be the same as the dimensionality of the data matrix. Categorical dimensions should take integer values between 1 and the number of categories. It is expected that each row of the matrix corresponds to a single data point, unlesspoints_are_rows
is set tofalse
when calling mlpack bindings.<Model> (mlpack model)
: An mlpack model pointer.<Model>
refers to the type of model that is being stored, so, e.g., forCF()
, the type will beCFModel
. This type holds a pointer to C++ memory containing the mlpack model. Note that this means the mlpack model itself cannot be easily inspected in Julia. However, the pointer can be passed to subsequent calls to mlpack functions, and can be serialized and deserialized via either theSerialization
package, or themlpack.serialize_bin()
andmlpack.deserialize_bin()
functions.
🔗 approx_kfn()
Approximate furthest neighbor search
julia> using mlpack: approx_kfn
julia> distances, neighbors, output_model = approx_kfn( ;
algorithm="ds", calculate_error=false, exact_distances=zeros(0, 0),
input_model=nothing, k=0, num_projections=5, num_tables=5,
query=zeros(0, 0), reference=zeros(0, 0), verbose=false)
An implementation of two strategies for furthest neighbor search. This can be used to compute the furthest neighbor of query point(s) from a set of points; furthest neighbor models can be saved and reused with future query point(s). Detailed documentation.
🔗 Input options
name  type  description  default 

algorithm 
String 
Algorithm to use: ‘ds’ or ‘qdafn’.  "ds" 
calculate_error 
Bool 
If set, calculate the average distance error for the first furthest neighbor only.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
exact_distances 
Float64 matrixlike 
Matrix containing exact distances to furthest neighbors; this can be used to avoid explicit calculation when –calculate_error is set.  zeros(0, 0) 
input_model 
ApproxKFNModel 
File containing input model.  nothing 
k 
Int 
Number of furthest neighbors to search for.  0 
num_projections 
Int 
Number of projections to use in each hash table.  5 
num_tables 
Int 
Number of hash tables to use.  5 
query 
Float64 matrixlike 
Matrix containing query points.  zeros(0, 0) 
reference 
Float64 matrixlike 
Matrix containing the reference dataset.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

distances 
Float64 matrixlike 
Matrix to save furthest neighbor distances to. 
neighbors 
Int matrixlike 
Matrix to save neighbor indices to. 
output_model 
ApproxKFNModel 
File to save output model to. 
🔗 Detailed documentation
This program implements two strategies for furthest neighbor search. These strategies are:
 The ‘qdafn’ algorithm from “Approximate Furthest Neighbor in High Dimensions” by R. Pagh, F. Silvestri, J. Sivertsen, and M. Skala, in Similarity Search and Applications 2015 (SISAP).
 The ‘DrusillaSelect’ algorithm from “Fast approximate furthest neighbors with datadependent candidate selection”, by R.R. Curtin and A.B. Gardner, in Similarity Search and Applications 2016 (SISAP).
These two strategies give approximate results for the furthest neighbor search problem and can be used as fast replacements for other furthest neighbor techniques such as those found in the mlpack_kfn program. Note that typically, the ‘ds’ algorithm requires far fewer tables and projections than the ‘qdafn’ algorithm.
Specify a reference set (set to search in) with reference
, specify a query set with query
, and specify algorithm parameters with num_tables
and num_projections
(or don’t and defaults will be used). The algorithm to be used (either ‘ds’—the default—or ‘qdafn’) may be specified with algorithm
. Also specify the number of neighbors to search for with k
.
Note that for ‘qdafn’ in lower dimensions, num_projections
may need to be set to a high value in order to return results for each query point.
If no query set is specified, the reference set will be used as the query set. The output_model
output parameter may be used to store the built model, and an input model may be loaded instead of specifying a reference set with the input_model
option.
Results for each query point can be stored with the neighbors
and distances
output parameters. Each row of these output matrices holds the k distances or neighbor indices for each query point.
🔗 Example
For example, to find the 5 approximate furthest neighbors with reference_set
as the reference set and query_set
as the query set using DrusillaSelect, storing the furthest neighbor indices to neighbors
and the furthest neighbor distances to distances
, one could call
julia> using CSV
julia> query_set = CSV.read("query_set.csv")
julia> reference_set = CSV.read("reference_set.csv")
julia> distances, neighbors, _ = approx_kfn(algorithm="ds", k=5,
query=query_set, reference=reference_set)
and to perform approximate allfurthestneighbors search with k=1 on the set data
storing only the furthest neighbor distances to distances
, one could call
julia> using CSV
julia> reference_set = CSV.read("reference_set.csv")
julia> distances, _, _ = approx_kfn(k=1, reference=reference_set)
A trained model can be reused. If a model has been previously saved to model
, then we may find 3 approximate furthest neighbors on a query set new_query_set
using that model and store the furthest neighbor indices into neighbors
by calling
julia> using CSV
julia> new_query_set = CSV.read("new_query_set.csv")
julia> _, neighbors, _ = approx_kfn(input_model=model, k=3,
query=new_query_set)
🔗 See also
 kfurthestneighbor search
 knearestneighbor search
 Fast approximate furthest neighbors with datadependent candidate selection (pdf)
 Approximate furthest neighbor in high dimensions (pdf)
 QDAFN class documentation
 DrusillaSelect class documentation
🔗 bayesian_linear_regression()
BayesianLinearRegression
julia> using mlpack: bayesian_linear_regression
julia> output_model, predictions, stds = bayesian_linear_regression( ;
center=false, input=zeros(0, 0), input_model=nothing,
responses=Float64[], scale=false, test=zeros(0, 0), verbose=false)
An implementation of the bayesian linear regression. Detailed documentation.
🔗 Input options
name  type  description  default 

center 
Bool 
Center the data and fit the intercept if enabled.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Matrix of covariates (X).  zeros(0, 0) 
input_model 
BayesianLinearRegression 
Trained BayesianLinearRegression model to use.  nothing 
responses 
Float64 vectorlike 
Matrix of responses/observations (y).  Float64[] 
scale 
Bool 
Scale each feature by their standard deviations if enabled.  false 
test 
Float64 matrixlike 
Matrix containing points to regress on (test points).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
BayesianLinearRegression 
Output BayesianLinearRegression model. 
predictions 
Float64 matrixlike 
If –test_file is specified, this file is where the predicted responses will be saved. 
stds 
Float64 matrixlike 
If specified, this is where the standard deviations of the predictive distribution will be saved. 
🔗 Detailed documentation
An implementation of the bayesian linear regression. This model is a probabilistic view and implementation of the linear regression. The final solution is obtained by computing a posterior distribution from gaussian likelihood and a zero mean gaussian isotropic prior distribution on the solution. Optimization is AUTOMATIC and does not require cross validation. The optimization is performed by maximization of the evidence function. Parameters are tuned during the maximization of the marginal likelihood. This procedure includes the Ockham’s razor that penalizes over complex solutions.
This program is able to train a Bayesian linear regression model or load a model from file, output regression predictions for a test set, and save the trained model to a file.
To train a BayesianLinearRegression model, the input
and responses
parameters must be given. The center
and scale
parameters control the centering and the normalizing options. A trained model can be saved with the output_model
. If no training is desired at all, a model can be passed via the input_model
parameter.
The program can also provide predictions for test data using either the trained model or the given input model. Test points can be specified with the test
parameter. Predicted responses to the test points can be saved with the predictions
output parameter. The corresponding standard deviation can be save by precising the stds
parameter.
🔗 Example
For example, the following command trains a model on the data data
and responses responses
with center set to true and scale set to false (so, Bayesian linear regression is being solved, and then the model is saved to blr_model
:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> responses = CSV.read("responses.csv")
julia> blr_model, _, _ = bayesian_linear_regression(center=1,
input=data, responses=responses, scale=0)
The following command uses the blr_model
to provide predicted responses for the data test
and save those responses to test_predictions
:
julia> using CSV
julia> test = CSV.read("test.csv")
julia> _, test_predictions, _ =
bayesian_linear_regression(input_model=blr_model, test=test)
Because the estimator computes a predictive distribution instead of a simple point estimate, the stds
parameter allows one to save the prediction uncertainties:
julia> using CSV
julia> test = CSV.read("test.csv")
julia> _, test_predictions, stds =
bayesian_linear_regression(input_model=blr_model, test=test)
🔗 See also
 Bayesian Interpolation
 Bayesian Linear Regression, Section 3.3
 BayesianLinearRegression C++ class documentation
🔗 cf()
Collaborative Filtering
julia> using mlpack: cf
julia> output, output_model = cf( ;
algorithm="NMF",
all_user_recommendations=false,
input_model=nothing, interpolation="average",
iteration_only_termination=false,
max_iterations=1000, min_residue=1e05,
neighbor_search="euclidean", neighborhood=5,
normalization="none", query=zeros(Int, 0, 0),
rank=0, recommendations=5, seed=0,
test=zeros(0, 0), training=zeros(0, 0),
verbose=false)
An implementation of several collaborative filtering (CF) techniques for recommender systems. This can be used to train a new CF model, or use an existing CF model to compute recommendations. Detailed documentation.
🔗 Input options
name  type  description  default 

algorithm 
String 
Algorithm used for matrix factorization.  "NMF" 
all_user_recommendations 
Bool 
Generate recommendations for all users.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
CFModel 
Trained CF model to load.  nothing 
interpolation 
String 
Algorithm used for weight interpolation.  "average" 
iteration_only_termination 
Bool 
Terminate only when the maximum number of iterations is reached.  false 
max_iterations 
Int 
Maximum number of iterations. If set to zero, there is no limit on the number of iterations.  1000 
min_residue 
Float64 
Residue required to terminate the factorization (lower values generally mean better fits).  1e05 
neighbor_search 
String 
Algorithm used for neighbor search.  "euclidean" 
neighborhood 
Int 
Size of the neighborhood of similar users to consider for each query user.  5 
normalization 
String 
Normalization performed on the ratings.  "none" 
query 
Int matrixlike 
List of query users for which recommendations should be generated.  zeros(Int, 0, 0) 
rank 
Int 
Rank of decomposed matrices (if 0, a heuristic is used to estimate the rank).  0 
recommendations 
Int 
Number of recommendations to generate for each query user.  5 
seed 
Int 
Set the random seed (0 uses std::time(NULL)).  0 
test 
Float64 matrixlike 
Test set to calculate RMSE on.  zeros(0, 0) 
training 
Float64 matrixlike 
Input dataset to perform CF on.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Int matrixlike 
Matrix that will store output recommendations. 
output_model 
CFModel 
Output for trained CF model. 
🔗 Detailed documentation
This program performs collaborative filtering (CF) on the given dataset. Given a list of user, item and preferences (the training
parameter), the program will perform a matrix decomposition and then can perform a series of actions related to collaborative filtering. Alternately, the program can load an existing saved CF model with the input_model
parameter and then use that model to provide recommendations or predict values.
The input matrix should be a 3dimensional matrix of ratings, where the first dimension is the user, the second dimension is the item, and the third dimension is that user’s rating of that item. Both the users and items should be numeric indices, not names. The indices are assumed to start from 0.
A set of query users for which recommendations can be generated may be specified with the query
parameter; alternately, recommendations may be generated for every user in the dataset by specifying the all_user_recommendations
parameter. In addition, the number of recommendations per user to generate can be specified with the recommendations
parameter, and the number of similar users (the size of the neighborhood) to be considered when generating recommendations can be specified with the neighborhood
parameter.
For performing the matrix decomposition, the following optimization algorithms can be specified via the algorithm
parameter:
 ‘RegSVD’ – Regularized SVD using a SGD optimizer
 ‘NMF’ – Nonnegative matrix factorization with alternating least squares update rules
 ‘BatchSVD’ – SVD batch learning
 ‘SVDIncompleteIncremental’ – SVD incomplete incremental learning
 ‘SVDCompleteIncremental’ – SVD complete incremental learning
 ‘BiasSVD’ – Bias SVD using a SGD optimizer
 ‘SVDPP’ – SVD++ using a SGD optimizer
 ‘RandSVD’ – RandomizedSVD learning
 ‘QSVD’ – QuicSVD learning
 ‘BKSVD’ – Block Krylov SVD learning
The following neighbor search algorithms can be specified via the neighbor_search
parameter:
 ‘cosine’ – Cosine Search Algorithm
 ‘euclidean’ – Euclidean Search Algorithm
 ‘pearson’ – Pearson Search Algorithm
The following weight interpolation algorithms can be specified via the interpolation
parameter:
 ‘average’ – Average Interpolation Algorithm
 ‘regression’ – Regression Interpolation Algorithm
 ‘similarity’ – Similarity Interpolation Algorithm
The following ranking normalization algorithms can be specified via the normalization
parameter:
 ‘none’ – No Normalization
 ‘item_mean’ – Item Mean Normalization
 ‘overall_mean’ – Overall Mean Normalization
 ‘user_mean’ – User Mean Normalization
 ‘z_score’ – ZScore Normalization
A trained model may be saved to with the output_model
output parameter.
🔗 Example
To train a CF model on a dataset training_set
using NMF for decomposition and saving the trained model to model
, one could call:
julia> using CSV
julia> training_set = CSV.read("training_set.csv")
julia> _, model = cf(algorithm="NMF", training=training_set)
Then, to use this model to generate recommendations for the list of users in the query set users
, storing 5 recommendations in recommendations
, one could call
julia> using CSV
julia> users = CSV.read("users.csv"; type=Int)
julia> recommendations, _ = cf(input_model=model, query=users,
recommendations=5)
🔗 See also
 Collaborative Filtering on Wikipedia
 Matrix factorization on Wikipedia
 Matrix factorization techniques for recommender systems (pdf)
 CFType class documentation
🔗 dbscan()
DBSCAN clustering
julia> using mlpack: dbscan
julia> assignments, centroids = dbscan(input; epsilon=1, min_size=5,
naive=false, selection_type="ordered", single_mode=false,
tree_type="kd", verbose=false)
An implementation of DBSCAN clustering. Given a dataset, this can compute and return a clustering of that dataset. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
epsilon 
Float64 
Radius of each range search.  1 
input 
Float64 matrixlike 
Input dataset to cluster.  **** 
min_size 
Int 
Minimum number of points for a cluster.  5 
naive 
Bool 
If set, bruteforce range search (not treebased) will be used.  false 
selection_type 
String 
If using point selection policy, the type of selection to use (‘ordered’, ‘random’).  "ordered" 
single_mode 
Bool 
If set, singletree range search (not dualtree) will be used.  false 
tree_type 
String 
If using singletree or dualtree search, the type of tree to use (‘kd’, ‘r’, ‘rstar’, ‘x’, ‘hilbertr’, ‘rplus’, ‘rplusplus’, ‘cover’, ‘ball’).  "kd" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

assignments 
Int vectorlike 
Output matrix for assignments of each point. 
centroids 
Float64 matrixlike 
Matrix to save output centroids to. 
🔗 Detailed documentation
This program implements the DBSCAN algorithm for clustering using accelerated treebased range search. The type of tree that is used may be parameterized, or bruteforce range search may also be used.
The input dataset to be clustered may be specified with the input
parameter; the radius of each range search may be specified with the epsilon
parameters, and the minimum number of points in a cluster may be specified with the min_size
parameter.
The assignments
and centroids
output parameters may be used to save the output of the clustering. assignments
contains the cluster assignments of each point, and centroids
contains the centroids of each cluster.
The range search may be controlled with the tree_type
, single_mode
, and naive
parameters. tree_type
can control the type of tree used for range search; this can take a variety of values: ‘kd’, ‘r’, ‘rstar’, ‘x’, ‘hilbertr’, ‘rplus’, ‘rplusplus’, ‘cover’, ‘ball’. The single_mode
parameter will force singletree search (as opposed to the default dualtree search), and ‘naive
will force bruteforce range search.
🔗 Example
An example usage to run DBSCAN on the dataset in input
with a radius of 0.5 and a minimum cluster size of 5 is given below:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> _, _ = dbscan(input; epsilon=0.5, min_size=5)
🔗 See also
 DBSCAN on Wikipedia
 A densitybased algorithm for discovering clusters in large spatial databases with noise (pdf)
 DBSCAN class documentation
🔗 decision_tree()
Decision tree
julia> using mlpack: decision_tree
julia> output_model, predictions, probabilities = decision_tree( ;
input_model=nothing, labels=Int[], maximum_depth=0,
minimum_gain_split=1e07, minimum_leaf_size=20,
print_training_accuracy=false, print_training_error=false,
test=zeros(0, 0), test_labels=Int[], training=zeros(0, 0),
verbose=false, weights=zeros(0, 0))
An implementation of an ID3style decision tree for classification, which supports categorical data. Given labeled data with numeric or categorical features, a decision tree can be trained and saved; or, an existing decision tree can be used for classification on new points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
DecisionTreeModel 
Pretrained decision tree, to be used with test points.  nothing 
labels 
Int vectorlike 
Training labels.  Int[] 
maximum_depth 
Int 
Maximum depth of the tree (0 means no limit).  0 
minimum_gain_split 
Float64 
Minimum gain for node splitting.  1e07 
minimum_leaf_size 
Int 
Minimum number of points in a leaf.  20 
print_training_accuracy 
Bool 
Print the training accuracy.  false 
print_training_error 
Bool 
Print the training error (deprecated; will be removed in mlpack 4.0.0).  false 
test 
Tuple{Array{Bool, 1}, Array{Float64, 2}} 
Testing dataset (may be categorical).  zeros(0, 0) 
test_labels 
Int vectorlike 
Test point labels, if accuracy calculation is desired.  Int[] 
training 
Tuple{Array{Bool, 1}, Array{Float64, 2}} 
Training dataset (may be categorical).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
weights 
Float64 matrixlike 
The weight of labels  zeros(0, 0) 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
DecisionTreeModel 
Output for trained decision tree. 
predictions 
Int vectorlike 
Class predictions for each test point. 
probabilities 
Float64 matrixlike 
Class probabilities for each test point. 
🔗 Detailed documentation
Train and evaluate using a decision tree. Given a dataset containing numeric or categorical features, and associated labels for each point in the dataset, this program can train a decision tree on that data.
The training set and associated labels are specified with the training
and labels
parameters, respectively. The labels should be in the range [0, num_classes  1]
. Optionally, if labels
is not specified, the labels are assumed to be the last dimension of the training dataset.
When a model is trained, the output_model
output parameter may be used to save the trained model. A model may be loaded for predictions with the input_model
parameter. The input_model
parameter may not be specified when the training
parameter is specified. The minimum_leaf_size
parameter specifies the minimum number of training points that must fall into each leaf for it to be split. The minimum_gain_split
parameter specifies the minimum gain that is needed for the node to split. The maximum_depth
parameter specifies the maximum depth of the tree. If print_training_error
is specified, the training error will be printed.
Test data may be specified with the test
parameter, and if performance numbers are desired for that test set, labels may be specified with the test_labels
parameter. Predictions for each test point may be saved via the predictions
output parameter. Class probabilities for each prediction may be saved with the probabilities
output parameter.
🔗 Example
For example, to train a decision tree with a minimum leaf size of 20 on the dataset contained in data
with labels labels
, saving the output model to tree
and printing the training error, one could call
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> tree, _, _ = decision_tree(labels=labels,
minimum_gain_split=0.001, minimum_leaf_size=20,
print_training_accuracy=1, training=data)
Then, to use that model to classify points in test_set
and print the test error given the labels test_labels
using that model, while saving the predictions for each point to predictions
, one could call
julia> using CSV
julia> test_set = CSV.read("test_set.csv")
julia> test_labels = CSV.read("test_labels.csv"; type=Int)
julia> _, predictions, _ = decision_tree(input_model=tree,
test=test_set, test_labels=test_labels)
🔗 See also
 Random forest
 Decision trees on Wikipedia
 Induction of Decision Trees (pdf)
 DecisionTree C++ class documentation
🔗 det()
Density Estimation With Density Estimation Trees
julia> using mlpack: det
julia> output_model, tag_counters_file, tag_file, test_set_estimates,
training_set_estimates, vi = det( ; folds=10, input_model=nothing,
max_leaf_size=10, min_leaf_size=5, path_format="lr",
skip_pruning=false, test=zeros(0, 0), training=zeros(0, 0),
verbose=false)
An implementation of density estimation trees for the density estimation task. Density estimation trees can be trained or used to predict the density at locations given by query points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
folds 
Int 
The number of folds of crossvalidation to perform for the estimation (0 is LOOCV)  10 
input_model 
DTree 
Trained density estimation tree to load.  nothing 
max_leaf_size 
Int 
The maximum size of a leaf in the unpruned, fully grown DET.  10 
min_leaf_size 
Int 
The minimum size of a leaf in the unpruned, fully grown DET.  5 
path_format 
String 
The format of path printing: ‘lr’, ‘idlr’, or ‘lrid’.  "lr" 
skip_pruning 
Bool 
Whether to bypass the pruning process and output the unpruned tree only.  false 
test 
Float64 matrixlike 
A set of test points to estimate the density of.  zeros(0, 0) 
training 
Float64 matrixlike 
The data set on which to build a density estimation tree.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
DTree 
Output to save trained density estimation tree to. 
tag_counters_file 
String 
The file to output the number of points that went to each leaf. 
tag_file 
String 
The file to output the tags (and possibly paths) for each sample in the test set. 
test_set_estimates 
Float64 matrixlike 
The output estimates on the test set from the final optimally pruned tree. 
training_set_estimates 
Float64 matrixlike 
The output density estimates on the training set from the final optimally pruned tree. 
vi 
Float64 matrixlike 
The output variable importance values for each feature. 
🔗 Detailed documentation
This program performs a number of functions related to Density Estimation Trees. The optimal Density Estimation Tree (DET) can be trained on a set of data (specified by training
) using crossvalidation (with number of folds specified with the folds
parameter). This trained density estimation tree may then be saved with the output_model
output parameter.
The variable importances (that is, the feature importance values for each dimension) may be saved with the vi
output parameter, and the density estimates for each training point may be saved with the training_set_estimates
output parameter.
Enabling path printing for each node outputs the path from the root node to a leaf for each entry in the test set, or training set (if a test set is not provided). Strings like ‘LRLRLR’ (indicating that traversal went to the left child, then the right child, then the left child, and so forth) will be output. If ‘lrid’ or ‘idlr’ are given as the path_format
parameter, then the ID (tag) of every node along the path will be printed after or before the L or R character indicating the direction of traversal, respectively.
This program also can provide density estimates for a set of test points, specified in the test
parameter. The density estimation tree used for this task will be the tree that was trained on the given training points, or a tree given as the parameter input_model
. The density estimates for the test points may be saved using the test_set_estimates
output parameter.
🔗 See also
🔗 emst()
Fast Euclidean Minimum Spanning Tree
julia> using mlpack: emst
julia> output = emst(input; leaf_size=1, naive=false,
verbose=false)
An implementation of the DualTree Boruvka algorithm for computing the Euclidean minimum spanning tree of a set of input points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Input data matrix.  **** 
leaf_size 
Int 
Leaf size in the kdtree. Oneelement leaves give the empirically best performance, but at the cost of greater memory requirements.  1 
naive 
Bool 
Compute the MST using O(n^2) naive algorithm.  false 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Output data. Stored as an edge list. 
🔗 Detailed documentation
This program can compute the Euclidean minimum spanning tree of a set of input points using the dualtree Boruvka algorithm.
The set to calculate the minimum spanning tree of is specified with the input
parameter, and the output may be saved with the output
output parameter.
The leaf_size
parameter controls the leaf size of the kdtree that is used to calculate the minimum spanning tree, and if the naive
option is given, then bruteforce search is used (this is typically much slower in low dimensions). The leaf size does not affect the results, but it may have some effect on the runtime of the algorithm.
🔗 Example
For example, the minimum spanning tree of the input dataset data
can be calculated with a leaf size of 20 and stored as spanning_tree
using the following command:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> spanning_tree = emst(data; leaf_size=20)
The output matrix is a threedimensional matrix, where each row indicates an edge. The first dimension corresponds to the lesser index of the edge; the second dimension corresponds to the greater index of the edge; and the third column corresponds to the distance between the two points.
🔗 See also
 Minimum spanning tree on Wikipedia
 Fast Euclidean Minimum Spanning Tree: Algorithm, Analysis, and Applications (pdf)
 DualTreeBoruvka class documentation
🔗 fastmks()
FastMKS (Fast MaxKernel Search)
julia> using mlpack: fastmks
julia> indices, kernels, output_model = fastmks( ; bandwidth=1,
base=2, degree=2, input_model=nothing, k=0, kernel="linear",
naive=false, offset=0, query=zeros(0, 0), reference=zeros(0, 0),
scale=1, single=false, verbose=false)
An implementation of the singletree and dualtree fast maxkernel search (FastMKS) algorithm. Given a set of reference points and a set of query points, this can find the reference point with maximum kernel value for each query point; trained models can be reused for future queries. Detailed documentation.
🔗 Input options
name  type  description  default 

bandwidth 
Float64 
Bandwidth (for Gaussian, Epanechnikov, and triangular kernels).  1 
base 
Float64 
Base to use during cover tree construction.  2 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
degree 
Float64 
Degree of polynomial kernel.  2 
input_model 
FastMKSModel 
Input FastMKS model to use.  nothing 
k 
Int 
Number of maximum kernels to find.  0 
kernel 
String 
Kernel type to use: ‘linear’, ‘polynomial’, ‘cosine’, ‘gaussian’, ‘epanechnikov’, ‘triangular’, ‘hyptan’.  "linear" 
naive 
Bool 
If true, O(n^2) naive mode is used for computation.  false 
offset 
Float64 
Offset of kernel (for polynomial and hyptan kernels).  0 
query 
Float64 matrixlike 
The query dataset.  zeros(0, 0) 
reference 
Float64 matrixlike 
The reference dataset.  zeros(0, 0) 
scale 
Float64 
Scale of kernel (for hyptan kernel).  1 
single 
Bool 
If true, singletree search is used (as opposed to dualtree search.  false 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

indices 
Int matrixlike 
Output matrix of indices. 
kernels 
Float64 matrixlike 
Output matrix of kernels. 
output_model 
FastMKSModel 
Output for FastMKS model. 
🔗 Detailed documentation
This program will find the k maximum kernels of a set of points, using a query set and a reference set (which can optionally be the same set). More specifically, for each point in the query set, the k points in the reference set with maximum kernel evaluations are found. The kernel function used is specified with the kernel
parameter.
🔗 Example
For example, the following command will calculate, for each point in the query set query
, the five points in the reference set reference
with maximum kernel evaluation using the linear kernel. The kernel evaluations may be saved with the kernels
output parameter and the indices may be saved with the indices
output parameter.
julia> using CSV
julia> reference = CSV.read("reference.csv")
julia> query = CSV.read("query.csv")
julia> indices, kernels, _ = fastmks(k=5, kernel="linear",
query=query, reference=reference)
The output matrices are organized such that row i and column j in the indices matrix corresponds to the index of the point in the reference set that has j’th largest kernel evaluation with the point in the query set with index i. Row i and column j in the kernels matrix corresponds to the kernel evaluation between those two points.
This program performs FastMKS using a cover tree. The base used to build the cover tree can be specified with the base
parameter.
🔗 See also
🔗 gmm_train()
Gaussian Mixture Model (GMM) Training
julia> using mlpack: gmm_train
julia> output_model = gmm_train(gaussians,
input; diagonal_covariance=false,
input_model=nothing, kmeans_max_iterations=1000,
max_iterations=250, no_force_positive=false,
noise=0, percentage=0.02, refined_start=false,
samplings=100, seed=0, tolerance=1e10,
trials=1, verbose=false)
An implementation of the EM algorithm for training Gaussian mixture models (GMMs). Given a dataset, this can train a GMM for future use with other tools. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
diagonal_covariance 
Bool 
Force the covariance of the Gaussians to be diagonal. This can accelerate training time significantly.  false 
gaussians 
Int 
Number of Gaussians in the GMM.  **** 
input 
Float64 matrixlike 
The training data on which the model will be fit.  **** 
input_model 
GMM 
Initial input GMM model to start training with.  nothing 
kmeans_max_iterations 
Int 
Maximum number of iterations for the kmeans algorithm (used to initialize EM).  1000 
max_iterations 
Int 
Maximum number of iterations of EM algorithm (passing 0 will run until convergence).  250 
no_force_positive 
Bool 
Do not force the covariance matrices to be positive definite.  false 
noise 
Float64 
Variance of zeromean Gaussian noise to add to data.  0 
percentage 
Float64 
If using –refined_start, specify the percentage of the dataset used for each sampling (should be between 0.0 and 1.0).  0.02 
refined_start 
Bool 
During the initialization, use refined initial positions for kmeans clustering (Bradley and Fayyad, 1998).  false 
samplings 
Int 
If using –refined_start, specify the number of samplings used for initial points.  100 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
tolerance 
Float64 
Tolerance for convergence of EM.  1e10 
trials 
Int 
Number of trials to perform in training GMM.  1 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
GMM 
Output for trained GMM model. 
🔗 Detailed documentation
This program takes a parametric estimate of a Gaussian mixture model (GMM) using the EM algorithm to find the maximum likelihood estimate. The model may be saved and reused by other mlpack GMM tools.
The input data to train on must be specified with the input
parameter, and the number of Gaussians in the model must be specified with the gaussians
parameter. Optionally, many trials with different random initializations may be run, and the result with highest loglikelihood on the training data will be taken. The number of trials to run is specified with the trials
parameter. By default, only one trial is run.
The tolerance for convergence and maximum number of iterations of the EM algorithm are specified with the tolerance
and max_iterations
parameters, respectively. The GMM may be initialized for training with another model, specified with the input_model
parameter. Otherwise, the model is initialized by running kmeans on the data. The kmeans clustering initialization can be controlled with the kmeans_max_iterations
, refined_start
, samplings
, and percentage
parameters. If refined_start
is specified, then the BradleyFayyad refined start initialization will be used. This can often lead to better clustering results.
The ‘diagonal_covariance’ flag will cause the learned covariances to be diagonal matrices. This significantly simplifies the model itself and causes training to be faster, but restricts the ability to fit more complex GMMs.
If GMM training fails with an error indicating that a covariance matrix could not be inverted, make sure that the no_force_positive
parameter is not specified. Alternately, adding a small amount of Gaussian noise (using the noise
parameter) to the entire dataset may help prevent Gaussians with zero variance in a particular dimension, which is usually the cause of noninvertible covariance matrices.
The no_force_positive
parameter, if set, will avoid the checks after each iteration of the EM algorithm which ensure that the covariance matrices are positive definite. Specifying the flag can cause faster runtime, but may also cause nonpositive definite covariance matrices, which will cause the program to crash.
🔗 Example
As an example, to train a 6Gaussian GMM on the data in data
with a maximum of 100 iterations of EM and 3 trials, saving the trained GMM to gmm
, the following command can be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> gmm = gmm_train(6, data; trials=3)
To retrain that GMM on another set of data data2
, the following command may be used:
julia> using CSV
julia> data2 = CSV.read("data2.csv")
julia> new_gmm = gmm_train(6, data2; input_model=gmm)
🔗 See also
🔗 gmm_generate()
GMM Sample Generator
julia> using mlpack: gmm_generate
julia> output = gmm_generate(input_model, samples;
seed=0, verbose=false)
A sample generator for pretrained GMMs. Given a pretrained GMM, this can sample new points randomly from that distribution. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
GMM 
Input GMM model to generate samples from.  **** 
samples 
Int 
Number of samples to generate.  **** 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save output samples in. 
🔗 Detailed documentation
This program is able to generate samples from a pretrained GMM (use gmm_train to train a GMM). The pretrained GMM must be specified with the input_model
parameter. The number of samples to generate is specified by the samples
parameter. Output samples may be saved with the output
output parameter.
🔗 Example
The following command can be used to generate 100 samples from the pretrained GMM gmm
and store those generated samples in samples
:
julia> samples = gmm_generate(gmm, 100)
🔗 See also
🔗 gmm_probability()
GMM Probability Calculator
julia> using mlpack: gmm_probability
julia> output = gmm_probability(input,
input_model; verbose=false)
A probability calculator for GMMs. Given a pretrained GMM and a set of points, this can compute the probability that each point is from the given GMM. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Input matrix to calculate probabilities of.  **** 
input_model 
GMM 
Input GMM to use as model.  **** 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to store calculated probabilities in. 
🔗 Detailed documentation
This program calculates the probability that given points came from a given GMM (that is, P(X  gmm)). The GMM is specified with the input_model
parameter, and the points are specified with the input
parameter. The output probabilities may be saved via the output
output parameter.
🔗 Example
So, for example, to calculate the probabilities of each point in points
coming from the pretrained GMM gmm
, while storing those probabilities in probs
, the following command could be used:
julia> using CSV
julia> points = CSV.read("points.csv")
julia> probs = gmm_probability(points, gmm)
🔗 See also
🔗 hmm_train()
Hidden Markov Model (HMM) Training
julia> using mlpack: hmm_train
julia> output_model = hmm_train(input_file;
batch=false, gaussians=0, input_model=nothing,
labels_file="", seed=0, states=0,
tolerance=1e05, type="gaussian",
verbose=false)
An implementation of training algorithms for Hidden Markov Models (HMMs). Given labeled or unlabeled data, an HMM can be trained for further use with other mlpack HMM tools. Detailed documentation.
🔗 Input options
name  type  description  default 

batch 
Bool 
If true, input_file (and if passed, labels_file) are expected to contain a list of files to use as input observation sequences (and label sequences).  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
gaussians 
Int 
Number of gaussians in each GMM (necessary when type is ‘gmm’).  0 
input_file 
String 
File containing input observations.  **** 
input_model 
HMMModel 
Preexisting HMM model to initialize training with.  nothing 
labels_file 
String 
Optional file of hidden states, used for labeled training.  "" 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
states 
Int 
Number of hidden states in HMM (necessary, unless model_file is specified).  0 
tolerance 
Float64 
Tolerance of the BaumWelch algorithm.  1e05 
type 
String 
Type of HMM: discrete  gaussian  diag_gmm  gmm.  "gaussian" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
HMMModel 
Output for trained HMM. 
🔗 Detailed documentation
This program allows a Hidden Markov Model to be trained on labeled or unlabeled data. It supports four types of HMMs: Discrete HMMs, Gaussian HMMs, GMM HMMs, or Diagonal GMM HMMs
Either one input sequence can be specified (with input_file
), or, a file containing files in which input sequences can be found (when input_file
andbatch
are used together). In addition, labels can be provided in the file specified by labels_file
, and if batch
is used, the file given to labels_file
should contain a list of files of labels corresponding to the sequences in the file given to input_file
.
The HMM is trained with the BaumWelch algorithm if no labels are provided. The tolerance of the BaumWelch algorithm can be set with the tolerance
option. By default, the transition matrix is randomly initialized and the emission distributions are initialized to fit the extent of the data.
Optionally, a precreated HMM model can be used as a guess for the transition matrix and emission probabilities; this is specifiable with output_model
.
🔗 See also
 hmm_generate()
 hmm_loglik()
 hmm_viterbi()
 Hidden Mixture Models on Wikipedia
 HMM class documentation
🔗 hmm_generate()
Hidden Markov Model (HMM) Sequence Generator
julia> using mlpack: hmm_generate
julia> output, state = hmm_generate(length, model; seed=0,
start_state=0, verbose=false)
A utility to generate random sequences from a pretrained Hidden Markov Model (HMM). The length of the desired sequence can be specified, and a random sequence of observations is returned. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
length 
Int 
Length of sequence to generate.  **** 
model 
HMMModel 
Trained HMM to generate sequences with.  **** 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
start_state 
Int 
Starting state of sequence.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save observation sequence to. 
state 
Int matrixlike 
Matrix to save hidden state sequence to. 
🔗 Detailed documentation
This utility takes an alreadytrained HMM, specified as the model
parameter, and generates a random observation sequence and hidden state sequence based on its parameters. The observation sequence may be saved with the output
output parameter, and the internal state sequence may be saved with the state
output parameter.
The state to start the sequence in may be specified with the start_state
parameter.
🔗 Example
For example, to generate a sequence of length 150 from the HMM hmm
and save the observation sequence to observations
and the hidden state sequence to states
, the following command may be used:
julia> observations, states = hmm_generate(150, hmm)
🔗 See also
🔗 hmm_loglik()
Hidden Markov Model (HMM) Sequence LogLikelihood
julia> using mlpack: hmm_loglik
julia> log_likelihood = hmm_loglik(input,
input_model; verbose=false)
A utility for computing the loglikelihood of a sequence for Hidden Markov Models (HMMs). Given a pretrained HMM and an observation sequence, this computes and returns the loglikelihood of that sequence being observed from that HMM. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
File containing observations,  **** 
input_model 
HMMModel 
File containing HMM.  **** 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

log_likelihood 
Float64 
Loglikelihood of the sequence. 
🔗 Detailed documentation
This utility takes an alreadytrained HMM, specified with the input_model
parameter, and evaluates the loglikelihood of a sequence of observations, given with the input
parameter. The computed loglikelihood is given as output.
🔗 Example
For example, to compute the loglikelihood of the sequence seq
with the pretrained HMM hmm
, the following command may be used:
julia> using CSV
julia> seq = CSV.read("seq.csv")
julia> _ = hmm_loglik(seq, hmm)
🔗 See also
🔗 hmm_viterbi()
Hidden Markov Model (HMM) Viterbi State Prediction
julia> using mlpack: hmm_viterbi
julia> output = hmm_viterbi(input, input_model;
verbose=false)
A utility for computing the most probable hidden state sequence for Hidden Markov Models (HMMs). Given a pretrained HMM and an observed sequence, this uses the Viterbi algorithm to compute and return the most probable hidden state sequence. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Matrix containing observations,  **** 
input_model 
HMMModel 
Trained HMM to use.  **** 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Int matrixlike 
File to save predicted state sequence to. 
🔗 Detailed documentation
This utility takes an alreadytrained HMM, specified as input_model
, and evaluates the most probable hidden state sequence of a given sequence of observations (specified as ‘input
, using the Viterbi algorithm. The computed state sequence may be saved using the output
output parameter.
🔗 Example
For example, to predict the state sequence of the observations obs
using the HMM hmm
, storing the predicted state sequence to states
, the following command could be used:
julia> using CSV
julia> obs = CSV.read("obs.csv")
julia> states = hmm_viterbi(obs, hmm)
🔗 See also
🔗 hoeffding_tree()
Hoeffding trees
julia> using mlpack: hoeffding_tree
julia> output_model, predictions, probabilities = hoeffding_tree( ;
batch_mode=false, bins=10, confidence=0.95, info_gain=false,
input_model=nothing, labels=Int[], max_samples=5000, min_samples=100,
numeric_split_strategy="binary", observations_before_binning=100,
passes=1, test=zeros(0, 0), test_labels=Int[], training=zeros(0, 0),
verbose=false)
An implementation of Hoeffding trees, a form of streaming decision tree for classification. Given labeled data, a Hoeffding tree can be trained and saved for later use, or a pretrained Hoeffding tree can be used for predicting the classifications of new points. Detailed documentation.
🔗 Input options
name  type  description  default 

batch_mode 
Bool 
If true, samples will be considered in batch instead of as a stream. This generally results in better trees but at the cost of memory usage and runtime.  false 
bins 
Int 
If the ‘domingos’ split strategy is used, this specifies the number of bins for each numeric split.  10 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
confidence 
Float64 
Confidence before splitting (between 0 and 1).  0.95 
info_gain 
Bool 
If set, information gain is used instead of Gini impurity for calculating Hoeffding bounds.  false 
input_model 
HoeffdingTreeModel 
Input trained Hoeffding tree model.  nothing 
labels 
Int vectorlike 
Labels for training dataset.  Int[] 
max_samples 
Int 
Maximum number of samples before splitting.  5000 
min_samples 
Int 
Minimum number of samples before splitting.  100 
numeric_split_strategy 
String 
The splitting strategy to use for numeric features: ‘domingos’ or ‘binary’.  "binary" 
observations_before_binning 
Int 
If the ‘domingos’ split strategy is used, this specifies the number of samples observed before binning is performed.  100 
passes 
Int 
Number of passes to take over the dataset.  1 
test 
Tuple{Array{Bool, 1}, Array{Float64, 2}} 
Testing dataset (may be categorical).  zeros(0, 0) 
test_labels 
Int vectorlike 
Labels of test data.  Int[] 
training 
Tuple{Array{Bool, 1}, Array{Float64, 2}} 
Training dataset (may be categorical).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
HoeffdingTreeModel 
Output for trained Hoeffding tree model. 
predictions 
Int vectorlike 
Matrix to output label predictions for test data into. 
probabilities 
Float64 matrixlike 
In addition to predicting labels, provide rediction probabilities in this matrix. 
🔗 Detailed documentation
This program implements Hoeffding trees, a form of streaming decision tree suited best for large (or streaming) datasets. This program supports both categorical and numeric data. Given an input dataset, this program is able to train the tree with numerous training options, and save the model to a file. The program is also able to use a trained model or a model from file in order to predict classes for a given test set.
The training file and associated labels are specified with the training
and labels
parameters, respectively. Optionally, if labels
is not specified, the labels are assumed to be the last dimension of the training dataset.
The training may be performed in batch mode (like a typical decision tree algorithm) by specifying the batch_mode
option, but this may not be the best option for large datasets.
When a model is trained, it may be saved via the output_model
output parameter. A model may be loaded from file for further training or testing with the input_model
parameter.
Test data may be specified with the test
parameter, and if performance statistics are desired for that test set, labels may be specified with the test_labels
parameter. Predictions for each test point may be saved with the predictions
output parameter, and class probabilities for each prediction may be saved with the probabilities
output parameter.
🔗 Example
For example, to train a Hoeffding tree with confidence 0.99 with data dataset
, saving the trained tree to tree
, the following command may be used:
julia> using CSV
julia> dataset = CSV.read("dataset.csv")
julia> tree, _, _ = hoeffding_tree(confidence=0.99,
training=dataset)
Then, this tree may be used to make predictions on the test set test_set
, saving the predictions into predictions
and the class probabilities into class_probs
with the following command:
julia> using CSV
julia> test_set = CSV.read("test_set.csv")
julia> _, predictions, class_probs =
hoeffding_tree(input_model=tree, test=test_set)
🔗 See also
 decision_tree()
 random_forest()
 Mining HighSpeed Data Streams (pdf)
 HoeffdingTree class documentation
🔗 kde()
Kernel Density Estimation
julia> using mlpack: kde
julia> output_model, predictions = kde( ; abs_error=0,
algorithm="dualtree", bandwidth=1, initial_sample_size=100,
input_model=nothing, kernel="gaussian", mc_break_coef=0.4,
mc_entry_coef=3, mc_probability=0.95, monte_carlo=false,
query=zeros(0, 0), reference=zeros(0, 0), rel_error=0.05,
tree="kdtree", verbose=false)
An implementation of kernel density estimation with dualtree algorithms. Given a set of reference points and query points and a kernel function, this can estimate the density function at the location of each query point using trees; trees that are built can be saved for later use. Detailed documentation.
🔗 Input options
name  type  description  default 

abs_error 
Float64 
Relative error tolerance for the prediction.  0 
algorithm 
String 
Algorithm to use for the prediction.(‘dualtree’, ‘singletree’).  "dualtree" 
bandwidth 
Float64 
Bandwidth of the kernel.  1 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
initial_sample_size 
Int 
Initial sample size for Monte Carlo estimations.  100 
input_model 
KDEModel 
Contains pretrained KDE model.  nothing 
kernel 
String 
Kernel to use for the prediction.(‘gaussian’, ‘epanechnikov’, ‘laplacian’, ‘spherical’, ‘triangular’).  "gaussian" 
mc_break_coef 
Float64 
Controls what fraction of the amount of node’s descendants is the limit for the sample size before it recurses.  0.4 
mc_entry_coef 
Float64 
Controls how much larger does the amount of node descendants has to be compared to the initial sample size in order to be a candidate for Monte Carlo estimations.  3 
mc_probability 
Float64 
Probability of the estimation being bounded by relative error when using Monte Carlo estimations.  0.95 
monte_carlo 
Bool 
Whether to use Monte Carlo estimations when possible.  false 
query 
Float64 matrixlike 
Query dataset to KDE on.  zeros(0, 0) 
reference 
Float64 matrixlike 
Input reference dataset use for KDE.  zeros(0, 0) 
rel_error 
Float64 
Relative error tolerance for the prediction.  0.05 
tree 
String 
Tree to use for the prediction.(‘kdtree’, ‘balltree’, ‘covertree’, ‘octree’, ‘rtree’).  "kdtree" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
KDEModel 
If specified, the KDE model will be saved here. 
predictions 
Float64 vectorlike 
Vector to store density predictions. 
🔗 Detailed documentation
This program performs a Kernel Density Estimation. KDE is a nonparametric way of estimating probability density function. For each query point the program will estimate its probability density by applying a kernel function to each reference point. The computational complexity of this is O(N^2) where there are N query points and N reference points, but this implementation will typically see better performance as it uses an approximate dual or single tree algorithm for acceleration.
Dual or single tree optimization avoids many barely relevant calculations (as kernel function values decrease with distance), so it is an approximate computation. You can specify the maximum relative error tolerance for each query value with rel_error
as well as the maximum absolute error tolerance with the parameter abs_error
. This program runs using an Euclidean metric. Kernel function can be selected using the kernel
option. You can also choose what which type of tree to use for the dualtree algorithm with tree
. It is also possible to select whether to use dualtree algorithm or singletree algorithm using the algorithm
option.
Monte Carlo estimations can be used to accelerate the KDE estimate when the Gaussian Kernel is used. This provides a probabilistic guarantee on the the error of the resulting KDE instead of an absolute guarantee.To enable Monte Carlo estimations, the monte_carlo
flag can be used, and success probability can be set with the mc_probability
option. It is possible to set the initial sample size for the Monte Carlo estimation using initial_sample_size
. This implementation will only consider a node, as a candidate for the Monte Carlo estimation, if its number of descendant nodes is bigger than the initial sample size. This can be controlled using a coefficient that will multiply the initial sample size and can be set using mc_entry_coef
. To avoid using the same amount of computations an exact approach would take, this program recurses the tree whenever a fraction of the amount of the node’s descendant points have already been computed. This fraction is set using mc_break_coef
.
🔗 Example
For example, the following will run KDE using the data in ref_data
for training and the data in qu_data
as query data. It will apply an Epanechnikov kernel with a 0.2 bandwidth to each reference point and use a KDTree for the dualtree optimization. The returned predictions will be within 5% of the real KDE value for each query point.
julia> using CSV
julia> ref_data = CSV.read("ref_data.csv")
julia> qu_data = CSV.read("qu_data.csv")
julia> _, out_data = kde(bandwidth=0.2, kernel="epanechnikov",
query=qu_data, reference=ref_data, rel_error=0.05, tree="kdtree")
the predicted density estimations will be stored in out_data
.
If no query
is provided, then KDE will be computed on the reference
dataset.
It is possible to select either a reference dataset or an input model but not both at the same time. If an input model is selected and parameter values are not set (e.g. bandwidth
) then default parameter values will be used.
In addition to the last program call, it is also possible to activate Monte Carlo estimations if a Gaussian kernel is used. This can provide faster results, but the KDE will only have a probabilistic guarantee of meeting the desired error bound (instead of an absolute guarantee). The following example will run KDE using a Monte Carlo estimation when possible. The results will be within a 5% of the real KDE value with a 95% probability. Initial sample size for the Monte Carlo estimation will be 200 points and a node will be a candidate for the estimation only when it contains 700 (i.e. 3.5200) points. If a node contains 700 points and 420 (i.e. 0.6700) have already been sampled, then the algorithm will recurse instead of keep sampling.
julia> using CSV
julia> ref_data = CSV.read("ref_data.csv")
julia> qu_data = CSV.read("qu_data.csv")
julia> _, out_data = kde(bandwidth=0.2, initial_sample_size=200,
kernel="gaussian", mc_break_coef=0.6, mc_entry_coef=3.5,
mc_probability=0.95, monte_carlo=, query=qu_data,
reference=ref_data, rel_error=0.05, tree="kdtree")
🔗 See also
 knn()
 Kernel density estimation on Wikipedia
 TreeIndependent DualTree Algorithms
 Fast Highdimensional Kernel Summations Using the Monte Carlo Multipole Method
 KDE C++ class documentation
🔗 kernel_pca()
Kernel Principal Components Analysis
julia> using mlpack: kernel_pca
julia> output = kernel_pca(input, kernel;
bandwidth=1, center=false, degree=1, kernel_scale=1,
new_dimensionality=0, nystroem_method=false,
offset=0, sampling="kmeans", verbose=false)
An implementation of Kernel Principal Components Analysis (KPCA). This can be used to perform nonlinear dimensionality reduction or preprocessing on a given dataset. Detailed documentation.
🔗 Input options
name  type  description  default 

bandwidth 
Float64 
Bandwidth, for ‘gaussian’ and ‘laplacian’ kernels.  1 
center 
Bool 
If set, the transformed data will be centered about the origin.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
degree 
Float64 
Degree of polynomial, for ‘polynomial’ kernel.  1 
input 
Float64 matrixlike 
Input dataset to perform KPCA on.  **** 
kernel 
String 
The kernel to use; see the above documentation for the list of usable kernels.  **** 
kernel_scale 
Float64 
Scale, for ‘hyptan’ kernel.  1 
new_dimensionality 
Int 
If not 0, reduce the dimensionality of the output dataset by ignoring the dimensions with the smallest eigenvalues.  0 
nystroem_method 
Bool 
If set, the Nystroem method will be used.  false 
offset 
Float64 
Offset, for ‘hyptan’ and ‘polynomial’ kernels.  0 
sampling 
String 
Sampling scheme to use for the Nystroem method: ‘kmeans’, ‘random’, ‘ordered’  "kmeans" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save modified dataset to. 
🔗 Detailed documentation
This program performs Kernel Principal Components Analysis (KPCA) on the specified dataset with the specified kernel. This will transform the data onto the kernel principal components, and optionally reduce the dimensionality by ignoring the kernel principal components with the smallest eigenvalues.
For the case where a linear kernel is used, this reduces to regular PCA.
The kernels that are supported are listed below:

‘linear’: the standard linear dot product (same as normal PCA):
K(x, y) = x^T y

‘gaussian’: a Gaussian kernel; requires bandwidth:
K(x, y) = exp((\\ x  y \\ ^ 2) / (2 * (bandwidth ^ 2)))

‘polynomial’: polynomial kernel; requires offset and degree:
K(x, y) = (x^T y + offset) ^ degree

‘hyptan’: hyperbolic tangent kernel; requires scale and offset:
K(x, y) = tanh(scale * (x^T y) + offset)

‘laplacian’: Laplacian kernel; requires bandwidth:
K(x, y) = exp((\\ x  y \\) / bandwidth)

‘epanechnikov’: Epanechnikov kernel; requires bandwidth:
K(x, y) = max(0, 1  \\ x  y \\^2 / bandwidth^2)

‘cosine’: cosine distance:
K(x, y) = 1  (x^T y) / (\\ x \\ * \\ y \\)
The parameters for each of the kernels should be specified with the options bandwidth
, kernel_scale
, offset
, or degree
(or a combination of those parameters).
Optionally, the Nystroem method (“Using the Nystroem method to speed up kernel machines”, 2001) can be used to calculate the kernel matrix by specifying the nystroem_method
parameter. This approach works by using a subset of the data as basis to reconstruct the kernel matrix; to specify the sampling scheme, the sampling
parameter is used. The sampling scheme for the Nystroem method can be chosen from the following list: ‘kmeans’, ‘random’, ‘ordered’.
🔗 Example
For example, the following command will perform KPCA on the dataset input
using the Gaussian kernel, and saving the transformed data to transformed
:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> transformed = kernel_pca(input, "gaussian")
🔗 See also
 Kernel principal component analysis on Wikipedia
 Kernel Principal Component Analysis (pdf)
 KernelPCA class documentation
🔗 kmeans()
KMeans Clustering
julia> using mlpack: kmeans
julia> centroid, output = kmeans(clusters,
input; algorithm="naive",
allow_empty_clusters=false, in_place=false,
initial_centroids=zeros(0, 0),
kill_empty_clusters=false,
kmeans_plus_plus=false, labels_only=false,
max_iterations=1000, percentage=0.02,
refined_start=false, samplings=100, seed=0,
verbose=false)
An implementation of several strategies for efficient kmeans clustering. Given a dataset and a value of k, this computes and returns a kmeans clustering on that data. Detailed documentation.
🔗 Input options
name  type  description  default 

algorithm 
String 
Algorithm to use for the Lloyd iteration (‘naive’, ‘pellegmoore’, ‘elkan’, ‘hamerly’, ‘dualtree’, or ‘dualtreecovertree’).  "naive" 
allow_empty_clusters 
Bool 
Allow empty clusters to be persist.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
clusters 
Int 
Number of clusters to find (0 autodetects from initial centroids).  **** 
in_place 
Bool 
If specified, a column containing the learned cluster assignments will be added to the input dataset file. In this case, –output_file is overridden. (Do not use in Python.)  false 
initial_centroids 
Float64 matrixlike 
Start with the specified initial centroids.  zeros(0, 0) 
input 
Float64 matrixlike 
Input dataset to perform clustering on.  **** 
kill_empty_clusters 
Bool 
Remove empty clusters when they occur.  false 
kmeans_plus_plus 
Bool 
Use the kmeans++ initialization strategy to choose initial points.  false 
labels_only 
Bool 
Only output labels into output file.  false 
max_iterations 
Int 
Maximum number of iterations before kmeans terminates.  1000 
percentage 
Float64 
Percentage of dataset to use for each refined start sampling (use when –refined_start is specified).  0.02 
refined_start 
Bool 
Use the refined initial point strategy by Bradley and Fayyad to choose initial points.  false 
samplings 
Int 
Number of samplings to perform for refined start (use when –refined_start is specified).  100 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

centroid 
Float64 matrixlike 
If specified, the centroids of each cluster will be written to the given file. 
output 
Float64 matrixlike 
Matrix to store output labels or labeled data to. 
🔗 Detailed documentation
This program performs KMeans clustering on the given dataset. It can return the learned cluster assignments, and the centroids of the clusters. Empty clusters are not allowed by default; when a cluster becomes empty, the point furthest from the centroid of the cluster with maximum variance is taken to fill that cluster.
Optionally, the strategy to choose initial centroids can be specified. The kmeans++ algorithm can be used to choose initial centroids with the kmeans_plus_plus
parameter. The Bradley and Fayyad approach (“Refining initial points for kmeans clustering”, 1998) can be used to select initial points by specifying the refined_start
parameter. This approach works by taking random samplings of the dataset; to specify the number of samplings, the samplings
parameter is used, and to specify the percentage of the dataset to be used in each sample, the percentage
parameter is used (it should be a value between 0.0 and 1.0).
There are several options available for the algorithm used for each Lloyd iteration, specified with the algorithm
option. The standard O(kN) approach can be used (‘naive’). Other options include the PellegMoore treebased algorithm (‘pellegmoore’), Elkan’s triangleinequality based algorithm (‘elkan’), Hamerly’s modification to Elkan’s algorithm (‘hamerly’), the dualtree kmeans algorithm (‘dualtree’), and the dualtree kmeans algorithm using the cover tree (‘dualtreecovertree’).
The behavior for when an empty cluster is encountered can be modified with the allow_empty_clusters
option. When this option is specified and there is a cluster owning no points at the end of an iteration, that cluster’s centroid will simply remain in its position from the previous iteration. If the kill_empty_clusters
option is specified, then when a cluster owns no points at the end of an iteration, the cluster centroid is simply filled with DBL_MAX, killing it and effectively reducing k for the rest of the computation. Note that the default option when neither empty cluster option is specified can be timeconsuming to calculate; therefore, specifying either of these parameters will often accelerate runtime.
Initial clustering assignments may be specified using the initial_centroids
parameter, and the maximum number of iterations may be specified with the max_iterations
parameter.
🔗 Example
As an example, to use Hamerly’s algorithm to perform kmeans clustering with k=10 on the dataset data
, saving the centroids to centroids
and the assignments for each point to assignments
, the following command could be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> centroids, assignments = kmeans(10, data)
To run kmeans on that same dataset with initial centroids specified in initial
with a maximum of 500 iterations, storing the output centroids in final
the following command may be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> initial = CSV.read("initial.csv")
julia> final, _ = kmeans(10, data; initial_centroids=initial,
max_iterations=500)
🔗 See also
 dbscan()
 kmeans++
 Using the triangle inequality to accelerate kmeans (pdf)
 Making kmeans even faster (pdf)
 Accelerating exact kmeans algorithms with geometric reasoning (pdf)
 A dualtree algorithm for fast kmeans clustering with large k (pdf)
 KMeans class documentation
🔗 lars()
LARS
julia> using mlpack: lars
julia> output_model, output_predictions = lars( ; input=zeros(0, 0),
input_model=nothing, lambda1=0, lambda2=0, no_intercept=false,
no_normalize=false, responses=zeros(0, 0), test=zeros(0, 0),
use_cholesky=false, verbose=false)
An implementation of Least Angle Regression (Stagewise/laSso), also known as LARS. This can train a LARS/LASSO/Elastic Net model and use that model or a pretrained model to output regression predictions for a test set. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Matrix of covariates (X).  zeros(0, 0) 
input_model 
LARS 
Trained LARS model to use.  nothing 
lambda1 
Float64 
Regularization parameter for l1norm penalty.  0 
lambda2 
Float64 
Regularization parameter for l2norm penalty.  0 
no_intercept 
Bool 
Do not fit an intercept in the model.  false 
no_normalize 
Bool 
Do not normalize data to unit variance before modeling.  false 
responses 
Float64 matrixlike 
Matrix of responses/observations (y).  zeros(0, 0) 
test 
Float64 matrixlike 
Matrix containing points to regress on (test points).  zeros(0, 0) 
use_cholesky 
Bool 
Use Cholesky decomposition during computation rather than explicitly computing the full Gram matrix.  false 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
LARS 
Output LARS model. 
output_predictions 
Float64 matrixlike 
If –test_file is specified, this file is where the predicted responses will be saved. 
🔗 Detailed documentation
An implementation of LARS: Least Angle Regression (Stagewise/laSso). This is a stagewise homotopybased algorithm for L1regularized linear regression (LASSO) and L1+L2regularized linear regression (Elastic Net).
This program is able to train a LARS/LASSO/Elastic Net model or load a model from file, output regression predictions for a test set, and save the trained model to a file. The LARS algorithm is described in more detail below:
Let X be a matrix where each row is a point and each column is a dimension, and let y be a vector of targets.
The Elastic Net problem is to solve
min_beta 0.5  X * beta  y _2^2 + lambda_1 beta_1 + 0.5 lambda_2 beta_2^2
If lambda1 > 0 and lambda2 = 0, the problem is the LASSO. If lambda1 > 0 and lambda2 > 0, the problem is the Elastic Net. If lambda1 = 0 and lambda2 > 0, the problem is ridge regression. If lambda1 = 0 and lambda2 = 0, the problem is unregularized linear regression.
For efficiency reasons, it is not recommended to use this algorithm with lambda1
= 0. In that case, use the ‘linear_regression’ program, which implements both unregularized linear regression and ridge regression.
To train a LARS/LASSO/Elastic Net model, the input
and responses
parameters must be given. The lambda1
, lambda2
, and use_cholesky
parameters control the training options. A trained model can be saved with the output_model
. If no training is desired at all, a model can be passed via the input_model
parameter.
The program can also provide predictions for test data using either the trained model or the given input model. Test points can be specified with the test
parameter. Predicted responses to the test points can be saved with the output_predictions
output parameter.
🔗 Example
For example, the following command trains a model on the data data
and responses responses
with lambda1 set to 0.4 and lambda2 set to 0 (so, LASSO is being solved), and then the model is saved to lasso_model
:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> responses = CSV.read("responses.csv")
julia> lasso_model, _ = lars(input=data, lambda1=0.4, lambda2=0,
responses=responses)
The following command uses the lasso_model
to provide predicted responses for the data test
and save those responses to test_predictions
:
julia> using CSV
julia> test = CSV.read("test.csv")
julia> _, test_predictions = lars(input_model=lasso_model,
test=test)
🔗 See also
🔗 linear_svm()
Linear SVM is an L2regularized support vector machine.
julia> using mlpack: linear_svm
julia> output_model, predictions, probabilities = linear_svm( ;
delta=1, epochs=50, input_model=nothing, labels=Int[], lambda=0.0001,
max_iterations=10000, no_intercept=false, num_classes=0,
optimizer="lbfgs", seed=0, shuffle=false, step_size=0.01,
test=zeros(0, 0), test_labels=Int[], tolerance=1e10,
training=zeros(0, 0), verbose=false)
An implementation of linear SVM for multiclass classification. Given labeled data, a model can be trained and saved for future use; or, a pretrained model can be used to classify new points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
delta 
Float64 
Margin of difference between correct class and other classes.  1 
epochs 
Int 
Maximum number of full epochs over dataset for psgd  50 
input_model 
LinearSVMModel 
Existing model (parameters).  nothing 
labels 
Int vectorlike 
A matrix containing labels (0 or 1) for the points in the training set (y).  Int[] 
lambda 
Float64 
L2regularization parameter for training.  0.0001 
max_iterations 
Int 
Maximum iterations for optimizer (0 indicates no limit).  10000 
no_intercept 
Bool 
Do not add the intercept term to the model.  false 
num_classes 
Int 
Number of classes for classification; if unspecified (or 0), the number of classes found in the labels will be used.  0 
optimizer 
String 
Optimizer to use for training (‘lbfgs’ or ‘psgd’).  "lbfgs" 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
shuffle 
Bool 
Don’t shuffle the order in which data points are visited for parallel SGD.  false 
step_size 
Float64 
Step size for parallel SGD optimizer.  0.01 
test 
Float64 matrixlike 
Matrix containing test dataset.  zeros(0, 0) 
test_labels 
Int vectorlike 
Matrix containing test labels.  Int[] 
tolerance 
Float64 
Convergence tolerance for optimizer.  1e10 
training 
Float64 matrixlike 
A matrix containing the training set (the matrix of predictors, X).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
LinearSVMModel 
Output for trained linear svm model. 
predictions 
Int vectorlike 
If test data is specified, this matrix is where the predictions for the test set will be saved. 
probabilities 
Float64 matrixlike 
If test data is specified, this matrix is where the class probabilities for the test set will be saved. 
🔗 Detailed documentation
An implementation of linear SVMs that uses either LBFGS or parallel SGD (stochastic gradient descent) to train the model.
This program allows loading a linear SVM model (via the input_model
parameter) or training a linear SVM model given training data (specified with the training
parameter), or both those things at once. In addition, this program allows classification on a test dataset (specified with the test
parameter) and the classification results may be saved with the predictions
output parameter. The trained linear SVM model may be saved using the output_model
output parameter.
The training data, if specified, may have class labels as its last dimension. Alternately, the labels
parameter may be used to specify a separate vector of labels.
When a model is being trained, there are many options. L2 regularization (to prevent overfitting) can be specified with the lambda
option, and the number of classes can be manually specified with the num_classes
and if an intercept term is not desired in the model, the no_intercept
parameter can be specified.Margin of difference between correct class and other classes can be specified with the delta
option.The optimizer used to train the model can be specified with the optimizer
parameter. Available options are ‘psgd’ (parallel stochastic gradient descent) and ‘lbfgs’ (the LBFGS optimizer). There are also various parameters for the optimizer; the max_iterations
parameter specifies the maximum number of allowed iterations, and the tolerance
parameter specifies the tolerance for convergence. For the parallel SGD optimizer, the step_size
parameter controls the step size taken at each iteration by the optimizer and the maximum number of epochs (specified with epochs
). If the objective function for your data is oscillating between Inf and 0, the step size is probably too large. There are more parameters for the optimizers, but the C++ interface must be used to access these.
Optionally, the model can be used to predict the labels for another matrix of data points, if test
is specified. The test
parameter can be specified without the training
parameter, so long as an existing linear SVM model is given with the input_model
parameter. The output predictions from the linear SVM model may be saved with the predictions
parameter.
🔗 Example
As an example, to train a LinaerSVM on the data ‘data
’ with labels ‘labels
’ with L2 regularization of 0.1, saving the model to ‘lsvm_model
’, the following command may be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> lsvm_model, _, _ = linear_svm(delta=1, labels=labels,
lambda=0.1, num_classes=0, training=data)
Then, to use that model to predict classes for the dataset ‘test
’, storing the output predictions in ‘predictions
’, the following command may be used:
julia> using CSV
julia> test = CSV.read("test.csv")
julia> _, predictions, _ = linear_svm(input_model=lsvm_model,
test=test)
🔗 See also
🔗 lmnn()
Large Margin Nearest Neighbors (LMNN)
julia> using mlpack: lmnn
julia> centered_data, output, transformed_data = lmnn(input;
batch_size=50, center=false, distance=zeros(0, 0), k=1, labels=Int[],
linear_scan=false, max_iterations=100000, normalize=false,
optimizer="amsgrad", passes=50, print_accuracy=false, range=1, rank=0,
regularization=0.5, seed=0, step_size=0.01, tolerance=1e07,
verbose=false)
An implementation of Large Margin Nearest Neighbors (LMNN), a distance learning technique. Given a labeled dataset, this learns a transformation of the data that improves knearestneighbor performance; this can be useful as a preprocessing step. Detailed documentation.
🔗 Input options
name  type  description  default 

batch_size 
Int 
Batch size for minibatch SGD.  50 
center 
Bool 
Perform meancentering on the dataset. It is useful when the centroid of the data is far from the origin.  false 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
distance 
Float64 matrixlike 
Initial distance matrix to be used as starting point  zeros(0, 0) 
input 
Float64 matrixlike 
Input dataset to run LMNN on.  **** 
k 
Int 
Number of target neighbors to use for each datapoint.  1 
labels 
Int vectorlike 
Labels for input dataset.  Int[] 
linear_scan 
Bool 
Don’t shuffle the order in which data points are visited for SGD or minibatch SGD.  false 
max_iterations 
Int 
Maximum number of iterations for LBFGS (0 indicates no limit).  100000 
normalize 
Bool 
Use a normalized starting point for optimization. Itis useful for when points are far apart, or when SGD is returning NaN.  false 
optimizer 
String 
Optimizer to use; ‘amsgrad’, ‘bbsgd’, ‘sgd’, or ‘lbfgs’.  "amsgrad" 
passes 
Int 
Maximum number of full passes over dataset for AMSGrad, BB_SGD and SGD.  50 
print_accuracy 
Bool 
Print accuracies on initial and transformed dataset  false 
range 
Int 
Number of iterations after which impostors needs to be recalculated  1 
rank 
Int 
Rank of distance matrix to be optimized.  0 
regularization 
Float64 
Regularization for LMNN objective function  0.5 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
step_size 
Float64 
Step size for AMSGrad, BB_SGD and SGD (alpha).  0.01 
tolerance 
Float64 
Maximum tolerance for termination of AMSGrad, BB_SGD, SGD or LBFGS.  1e07 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

centered_data 
Float64 matrixlike 
Output matrix for meancentered dataset. 
output 
Float64 matrixlike 
Output matrix for learned distance matrix. 
transformed_data 
Float64 matrixlike 
Output matrix for transformed dataset. 
🔗 Detailed documentation
This program implements Large Margin Nearest Neighbors, a distance learning technique. The method seeks to improve knearestneighbor classification on a dataset. The method employes the strategy of reducing distance between similar labeled data points (a.k.a target neighbors) and increasing distance between differently labeled points (a.k.a impostors) using standard optimization techniques over the gradient of the distance between data points.
To work, this algorithm needs labeled data. It can be given as the last row of the input dataset (specified with input
), or alternatively as a separate matrix (specified with labels
). Additionally, a starting point for optimization (specified with distance
can be given, having (r x d) dimensionality. Here r should satisfy 1 <= r <= d, Consequently a LowRank matrix will be optimized. Alternatively, LowRank distance can be learned by specifying the rank
parameter (A LowRank matrix with uniformly distributed values will be used as initial learning point).
The program also requires number of targets neighbors to work with ( specified with k
), A regularization parameter can also be passed, It acts as a trade of between the pulling and pushing terms (specified with regularization
), In addition, this implementation of LMNN includes a parameter to decide the interval after which impostors must be recalculated (specified with range
).
Output can either be the learned distance matrix (specified with output
), or the transformed dataset (specified with transformed_data
), or both. Additionally meancentered dataset (specified with centered_data
) can be accessed given meancentering (specified with center
) is performed on the dataset. Accuracy on initial dataset and final transformed dataset can be printed by specifying the print_accuracy
parameter.
This implementation of LMNN uses AdaGrad, BigBatch_SGD, stochastic gradient descent, minibatch stochastic gradient descent, or the L_BFGS optimizer.
AdaGrad, specified by the value ‘adagrad’ for the parameter optimizer
, uses maximum of past squared gradients. It primarily on six parameters: the step size (specified with step_size
), the batch size (specified with batch_size
), the maximum number of passes (specified with passes
). Inaddition, a normalized starting point can be used by specifying the normalize
parameter.
BigBatch_SGD, specified by the value ‘bbsgd’ for the parameter optimizer
, depends primarily on four parameters: the step size (specified with step_size
), the batch size (specified with batch_size
), the maximum number of passes (specified with passes
). In addition, a normalized starting point can be used by specifying the normalize
parameter.
Stochastic gradient descent, specified by the value ‘sgd’ for the parameter optimizer
, depends primarily on three parameters: the step size (specified with step_size
), the batch size (specified with batch_size
), and the maximum number of passes (specified with passes
). In addition, a normalized starting point can be used by specifying the normalize
parameter. Furthermore, meancentering can be performed on the dataset by specifying the center
parameter.
The LBFGS optimizer, specified by the value ‘lbfgs’ for the parameter optimizer
, uses a backtracking line search algorithm to minimize a function. The following parameters are used by LBFGS: max_iterations
, tolerance
(the optimization is terminated when the gradient norm is below this value). For more details on the LBFGS optimizer, consult either the mlpack LBFGS documentation (in lbfgs.hpp) or the vast set of published literature on LBFGS. In addition, a normalized starting point can be used by specifying the normalize
parameter.
By default, the AMSGrad optimizer is used.
🔗 Example
Example  Let’s say we want to learn distance on iris dataset with number of targets as 3 using BigBatch_SGD optimizer. A simple call for the same will look like:
julia> using CSV
julia> iris = CSV.read("iris.csv")
julia> iris_labels = CSV.read("iris_labels.csv"; type=Int)
julia> _, output, _ = lmnn(iris; k=3, labels=iris_labels,
optimizer="bbsgd")
An another program call making use of range & regularization parameter with dataset having labels as last column can be made as:
julia> using CSV
julia> letter_recognition = CSV.read("letter_recognition.csv")
julia> _, output, _ = lmnn(letter_recognition; k=5, range=10,
regularization=0.4)
🔗 See also
 nca()
 Large margin nearest neighbor on Wikipedia
 Distance metric learning for large margin nearest neighbor classification (pdf)
 LMNN C++ class documentation
🔗 local_coordinate_coding()
Local Coordinate Coding
julia> using mlpack: local_coordinate_coding
julia> codes, dictionary, output_model = local_coordinate_coding( ;
atoms=0, initial_dictionary=zeros(0, 0), input_model=nothing,
lambda=0, max_iterations=0, normalize=false, seed=0, test=zeros(0, 0),
tolerance=0.01, training=zeros(0, 0), verbose=false)
An implementation of Local Coordinate Coding (LCC), a data transformation technique. Given input data, this transforms each point to be expressed as a linear combination of a few points in the dataset; once an LCC model is trained, it can be used to transform points later also. Detailed documentation.
🔗 Input options
name  type  description  default 

atoms 
Int 
Number of atoms in the dictionary.  0 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
initial_dictionary 
Float64 matrixlike 
Optional initial dictionary.  zeros(0, 0) 
input_model 
LocalCoordinateCoding 
Input LCC model.  nothing 
lambda 
Float64 
Weighted l1norm regularization parameter.  0 
max_iterations 
Int 
Maximum number of iterations for LCC (0 indicates no limit).  0 
normalize 
Bool 
If set, the input data matrix will be normalized before coding.  false 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
test 
Float64 matrixlike 
Test points to encode.  zeros(0, 0) 
tolerance 
Float64 
Tolerance for objective function.  0.01 
training 
Float64 matrixlike 
Matrix of training data (X).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

codes 
Float64 matrixlike 
Output codes matrix. 
dictionary 
Float64 matrixlike 
Output dictionary matrix. 
output_model 
LocalCoordinateCoding 
Output for trained LCC model. 
🔗 Detailed documentation
An implementation of Local Coordinate Coding (LCC), which codes data that approximately lives on a manifold using a variation of l1norm regularized sparse coding. Given a dense data matrix X with n points and d dimensions, LCC seeks to find a dense dictionary matrix D with k atoms in d dimensions, and a coding matrix Z with n points in k dimensions. Because of the regularization method used, the atoms in D should lie close to the manifold on which the data points lie.
The original data matrix X can then be reconstructed as D * Z. Therefore, this program finds a representation of each point in X as a sparse linear combination of atoms in the dictionary D.
The coding is found with an algorithm which alternates between a dictionary step, which updates the dictionary D, and a coding step, which updates the coding matrix Z.
To run this program, the input matrix X must be specified (with i), along with the number of atoms in the dictionary (k). An initial dictionary may also be specified with the initial_dictionary
parameter. The l1norm regularization parameter is specified with the lambda
parameter.
🔗 Example
For example, to run LCC on the dataset data
using 200 atoms and an l1regularization parameter of 0.1, saving the dictionary dictionary
and the codes into codes
, use
julia> using CSV
julia> data = CSV.read("data.csv")
julia> codes, dict, _ = local_coordinate_coding(atoms=200,
lambda=0.1, training=data)
The maximum number of iterations may be specified with the max_iterations
parameter. Optionally, the input data matrix X can be normalized before coding with the normalize
parameter.
An LCC model may be saved using the output_model
output parameter. Then, to encode new points from the dataset points
with the previously saved model lcc_model
, saving the new codes to new_codes
, the following command can be used:
julia> using CSV
julia> points = CSV.read("points.csv")
julia> new_codes, _, _ =
local_coordinate_coding(input_model=lcc_model, test=points)
🔗 See also
 sparse_coding()
 Nonlinear learning using local coordinate coding (pdf)
 LocalCoordinateCoding C++ class documentation
🔗 logistic_regression()
L2regularized Logistic Regression and Prediction
julia> using mlpack: logistic_regression
julia> output_model, predictions, probabilities = logistic_regression(
; batch_size=64, decision_boundary=0.5, input_model=nothing,
labels=Int[], lambda=0, max_iterations=10000, optimizer="lbfgs",
print_training_accuracy=false, step_size=0.01, test=zeros(0, 0),
tolerance=1e10, training=zeros(0, 0), verbose=false)
An implementation of L2regularized logistic regression for twoclass classification. Given labeled data, a model can be trained and saved for future use; or, a pretrained model can be used to classify new points. Detailed documentation.
🔗 Input options
name  type  description  default 

batch_size 
Int 
Batch size for SGD.  64 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
decision_boundary 
Float64 
Decision boundary for prediction; if the logistic function for a point is less than the boundary, the class is taken to be 0; otherwise, the class is 1.  0.5 
input_model 
LogisticRegression 
Existing model (parameters).  nothing 
labels 
Int vectorlike 
A matrix containing labels (0 or 1) for the points in the training set (y).  Int[] 
lambda 
Float64 
L2regularization parameter for training.  0 
max_iterations 
Int 
Maximum iterations for optimizer (0 indicates no limit).  10000 
optimizer 
String 
Optimizer to use for training (‘lbfgs’ or ‘sgd’).  "lbfgs" 
print_training_accuracy 
Bool 
If set, then the accuracy of the model on the training set will be printed (verbose must also be specified).  false 
step_size 
Float64 
Step size for SGD optimizer.  0.01 
test 
Float64 matrixlike 
Matrix containing test dataset.  zeros(0, 0) 
tolerance 
Float64 
Convergence tolerance for optimizer.  1e10 
training 
Float64 matrixlike 
A matrix containing the training set (the matrix of predictors, X).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
LogisticRegression 
Output for trained logistic regression model. 
predictions 
Int vectorlike 
If test data is specified, this matrix is where the predictions for the test set will be saved. 
probabilities 
Float64 matrixlike 
If test data is specified, this matrix is where the class probabilities for the test set will be saved. 
🔗 Detailed documentation
An implementation of L2regularized logistic regression using either the LBFGS optimizer or SGD (stochastic gradient descent). This solves the regression problem
y = (1 / 1 + e^(X * b)).
In this setting, y corresponds to class labels and X corresponds to data.
This program allows loading a logistic regression model (via the input_model
parameter) or training a logistic regression model given training data (specified with the training
parameter), or both those things at once. In addition, this program allows classification on a test dataset (specified with the test
parameter) and the classification results may be saved with the predictions
output parameter. The trained logistic regression model may be saved using the output_model
output parameter.
The training data, if specified, may have class labels as its last dimension. Alternately, the labels
parameter may be used to specify a separate matrix of labels.
When a model is being trained, there are many options. L2 regularization (to prevent overfitting) can be specified with the lambda
option, and the optimizer used to train the model can be specified with the optimizer
parameter. Available options are ‘sgd’ (stochastic gradient descent) and ‘lbfgs’ (the LBFGS optimizer). There are also various parameters for the optimizer; the max_iterations
parameter specifies the maximum number of allowed iterations, and the tolerance
parameter specifies the tolerance for convergence. For the SGD optimizer, the step_size
parameter controls the step size taken at each iteration by the optimizer. The batch size for SGD is controlled with the batch_size
parameter. If the objective function for your data is oscillating between Inf and 0, the step size is probably too large. There are more parameters for the optimizers, but the C++ interface must be used to access these.
For SGD, an iteration refers to a single point. So to take a single pass over the dataset with SGD, max_iterations
should be set to the number of points in the dataset.
Optionally, the model can be used to predict the responses for another matrix of data points, if test
is specified. The test
parameter can be specified without the training
parameter, so long as an existing logistic regression model is given with the input_model
parameter. The output predictions from the logistic regression model may be saved with the predictions
parameter.
This implementation of logistic regression does not support the general multiclass case but instead only the twoclass case. Any labels must be either 0 or 1. For more classes, see the softmax regression implementation.
🔗 Example
As an example, to train a logistic regression model on the data ‘data
’ with labels ‘labels
’ with L2 regularization of 0.1, saving the model to ‘lr_model
’, the following command may be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> lr_model, _, _ = logistic_regression(labels=labels,
lambda=0.1, print_training_accuracy=1, training=data)
Then, to use that model to predict classes for the dataset ‘test
’, storing the output predictions in ‘predictions
’, the following command may be used:
julia> using CSV
julia> test = CSV.read("test.csv")
julia> _, predictions, _ = logistic_regression(input_model=lr_model,
test=test)
🔗 See also
 softmax_regression()
 random_forest()
 Logistic regression on Wikipedia
 :LogisticRegression C++ class documentation
🔗 lsh()
KApproximateNearestNeighbor Search with LSH
julia> using mlpack: lsh
julia> distances, neighbors, output_model = lsh( ; bucket_size=500,
hash_width=0, input_model=nothing, k=0, num_probes=0, projections=10,
query=zeros(0, 0), reference=zeros(0, 0), second_hash_size=99901,
seed=0, tables=30, true_neighbors=zeros(Int, 0, 0), verbose=false)
An implementation of approximate knearestneighbor search with localitysensitive hashing (LSH). Given a set of reference points and a set of query points, this will compute the k approximate nearest neighbors of each query point in the reference set; models can be saved for future use. Detailed documentation.
🔗 Input options
name  type  description  default 

bucket_size 
Int 
The size of a bucket in the second level hash.  500 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
hash_width 
Float64 
The hash width for the firstlevel hashing in the LSH preprocessing. By default, the LSH class automatically estimates a hash width for its use.  0 
input_model 
LSHSearch 
Input LSH model.  nothing 
k 
Int 
Number of nearest neighbors to find.  0 
num_probes 
Int 
Number of additional probes for multiprobe LSH; if 0, traditional LSH is used.  0 
projections 
Int 
The number of hash functions for each table  10 
query 
Float64 matrixlike 
Matrix containing query points (optional).  zeros(0, 0) 
reference 
Float64 matrixlike 
Matrix containing the reference dataset.  zeros(0, 0) 
second_hash_size 
Int 
The size of the second level hash table.  99901 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
tables 
Int 
The number of hash tables to be used.  30 
true_neighbors 
Int matrixlike 
Matrix of true neighbors to compute recall with (the recall is printed when v is specified).  zeros(Int, 0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

distances 
Float64 matrixlike 
Matrix to output distances into. 
neighbors 
Int matrixlike 
Matrix to output neighbors into. 
output_model 
LSHSearch 
Output for trained LSH model. 
🔗 Detailed documentation
This program will calculate the k approximatenearestneighbors of a set of points using localitysensitive hashing. You may specify a separate set of reference points and query points, or just a reference set which will be used as both the reference and query set.
🔗 Example
For example, the following will return 5 neighbors from the data for each point in input
and store the distances in distances
and the neighbors in neighbors
:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> distances, neighbors, _ = lsh(k=5, reference=input)
The output is organized such that row i and column j in the neighbors output corresponds to the index of the point in the reference set which is the j’th nearest neighbor from the point in the query set with index i. Row j and column i in the distances output file corresponds to the distance between those two points.
Because this is approximatenearestneighbors search, results may be different from run to run. Thus, the seed
parameter can be specified to set the random seed.
This program also has many other parameters to control its functionality; see the parameterspecific documentation for more information.
🔗 See also
 knn()
 krann()
 Localitysensitive hashing on Wikipedia
 Localitysensitive hashing scheme based on pstable distributions(pdf)
 LSHSearch C++ class documentation
🔗 mean_shift()
Mean Shift Clustering
julia> using mlpack: mean_shift
julia> centroid, output = mean_shift(input; force_convergence=false,
in_place=false, labels_only=false, max_iterations=1000, radius=0,
verbose=false)
A fast implementation of meanshift clustering using dualtree range search. Given a dataset, this uses the mean shift algorithm to produce and return a clustering of the data. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
force_convergence 
Bool 
If specified, the mean shift algorithm will continue running regardless of max_iterations until the clusters converge.  false 
in_place 
Bool 
If specified, a column containing the learned cluster assignments will be added to the input dataset file. In this case, –output_file is overridden. (Do not use with Python.)  false 
input 
Float64 matrixlike 
Input dataset to perform clustering on.  **** 
labels_only 
Bool 
If specified, only the output labels will be written to the file specified by –output_file.  false 
max_iterations 
Int 
Maximum number of iterations before mean shift terminates.  1000 
radius 
Float64 
If the distance between two centroids is less than the given radius, one will be removed. A radius of 0 or less means an estimate will be calculated and used for the radius.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

centroid 
Float64 matrixlike 
If specified, the centroids of each cluster will be written to the given matrix. 
output 
Float64 matrixlike 
Matrix to write output labels or labeled data to. 
🔗 Detailed documentation
This program performs mean shift clustering on the given dataset, storing the learned cluster assignments either as a column of labels in the input dataset or separately.
The input dataset should be specified with the input
parameter, and the radius used for search can be specified with the radius
parameter. The maximum number of iterations before algorithm termination is controlled with the max_iterations
parameter.
The output labels may be saved with the output
output parameter and the centroids of each cluster may be saved with the centroid
output parameter.
🔗 Example
For example, to run mean shift clustering on the dataset data
and store the centroids to centroids
, the following command may be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> centroids, _ = mean_shift(data)
🔗 See also
 kmeans()
 dbscan()
 Mean shift on Wikipedia
 Mean Shift, Mode Seeking, and Clustering (pdf)
 mlpack::mean_shift::MeanShift C++ class documentation
🔗 nbc()
Parametric Naive Bayes Classifier
julia> using mlpack: nbc
julia> output, output_model, output_probs, predictions, probabilities
= nbc( ; incremental_variance=false, input_model=nothing,
labels=Int[], test=zeros(0, 0), training=zeros(0, 0), verbose=false)
An implementation of the Naive Bayes Classifier, used for classification. Given labeled data, an NBC model can be trained and saved, or, a pretrained model can be used for classification. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
incremental_variance 
Bool 
The variance of each class will be calculated incrementally.  false 
input_model 
NBCModel 
Input Naive Bayes model.  nothing 
labels 
Int vectorlike 
A file containing labels for the training set.  Int[] 
test 
Float64 matrixlike 
A matrix containing the test set.  zeros(0, 0) 
training 
Float64 matrixlike 
A matrix containing the training set.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Int vectorlike 
The matrix in which the predicted labels for the test set will be written (deprecated). 
output_model 
NBCModel 
File to save trained Naive Bayes model to. 
output_probs 
Float64 matrixlike 
The matrix in which the predicted probability of labels for the test set will be written (deprecated). 
predictions 
Int vectorlike 
The matrix in which the predicted labels for the test set will be written. 
probabilities 
Float64 matrixlike 
The matrix in which the predicted probability of labels for the test set will be written. 
🔗 Detailed documentation
This program trains the Naive Bayes classifier on the given labeled training set, or loads a model from the given model file, and then may use that trained model to classify the points in a given test set.
The training set is specified with the training
parameter. Labels may be either the last row of the training set, or alternately the labels
parameter may be specified to pass a separate matrix of labels.
If training is not desired, a preexisting model may be loaded with the input_model
parameter.
The incremental_variance
parameter can be used to force the training to use an incremental algorithm for calculating variance. This is slower, but can help avoid loss of precision in some cases.
If classifying a test set is desired, the test set may be specified with the test
parameter, and the classifications may be saved with the predictions
predictions parameter. If saving the trained model is desired, this may be done with the output_model
output parameter.
Note: the output
and output_probs
parameters are deprecated and will be removed in mlpack 4.0.0. Use predictions
and probabilities
instead.
🔗 Example
For example, to train a Naive Bayes classifier on the dataset data
with labels labels
and save the model to nbc_model
, the following command may be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> _, nbc_model, _, _, _ = nbc(labels=labels, training=data)
Then, to use nbc_model
to predict the classes of the dataset test_set
and save the predicted classes to predictions
, the following command may be used:
julia> using CSV
julia> test_set = CSV.read("test_set.csv")
julia> predictions, _, _, _, _ = nbc(input_model=nbc_model,
test=test_set)
🔗 See also
 softmax_regression()
 random_forest()
 Naive Bayes classifier on Wikipedia
 NaiveBayesClassifier C++ class documentation
🔗 nca()
Neighborhood Components Analysis (NCA)
julia> using mlpack: nca
julia> output = nca(input; armijo_constant=0.0001,
batch_size=50, labels=Int[], linear_scan=false,
max_iterations=500000, max_line_search_trials=50,
max_step=1e+20, min_step=1e20, normalize=false,
num_basis=5, optimizer="sgd", seed=0, step_size=0.01,
tolerance=1e07, verbose=false, wolfe=0.9)
An implementation of neighborhood components analysis, a distance learning technique that can be used for preprocessing. Given a labeled dataset, this uses NCA, which seeks to improve the knearestneighbor classification, and returns the learned distance metric. Detailed documentation.
🔗 Input options
name  type  description  default 

armijo_constant 
Float64 
Armijo constant for LBFGS.  0.0001 
batch_size 
Int 
Batch size for minibatch SGD.  50 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Input dataset to run NCA on.  **** 
labels 
Int vectorlike 
Labels for input dataset.  Int[] 
linear_scan 
Bool 
Don’t shuffle the order in which data points are visited for SGD or minibatch SGD.  false 
max_iterations 
Int 
Maximum number of iterations for SGD or LBFGS (0 indicates no limit).  500000 
max_line_search_trials 
Int 
Maximum number of line search trials for LBFGS.  50 
max_step 
Float64 
Maximum step of line search for LBFGS.  1e+20 
min_step 
Float64 
Minimum step of line search for LBFGS.  1e20 
normalize 
Bool 
Use a normalized starting point for optimization. This is useful for when points are far apart, or when SGD is returning NaN.  false 
num_basis 
Int 
Number of memory points to be stored for LBFGS.  5 
optimizer 
String 
Optimizer to use; ‘sgd’ or ‘lbfgs’.  "sgd" 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
step_size 
Float64 
Step size for stochastic gradient descent (alpha).  0.01 
tolerance 
Float64 
Maximum tolerance for termination of SGD or LBFGS.  1e07 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
wolfe 
Float64 
Wolfe condition parameter for LBFGS.  0.9 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Output matrix for learned distance matrix. 
🔗 Detailed documentation
This program implements Neighborhood Components Analysis, both a linear dimensionality reduction technique and a distance learning technique. The method seeks to improve knearestneighbor classification on a dataset by scaling the dimensions. The method is nonparametric, and does not require a value of k. It works by using stochastic (“soft”) neighbor assignments and using optimization techniques over the gradient of the accuracy of the neighbor assignments.
To work, this algorithm needs labeled data. It can be given as the last row of the input dataset (specified with input
), or alternatively as a separate matrix (specified with labels
).
This implementation of NCA uses stochastic gradient descent, minibatch stochastic gradient descent, or the L_BFGS optimizer. These optimizers do not guarantee global convergence for a nonconvex objective function (NCA’s objective function is nonconvex), so the final results could depend on the random seed or other optimizer parameters.
Stochastic gradient descent, specified by the value ‘sgd’ for the parameter optimizer
, depends primarily on three parameters: the step size (specified with step_size
), the batch size (specified with batch_size
), and the maximum number of iterations (specified with max_iterations
). In addition, a normalized starting point can be used by specifying the normalize
parameter, which is necessary if many warnings of the form ‘Denominator of p_i is 0!’ are given. Tuning the step size can be a tedious affair. In general, the step size is too large if the objective is not mostly uniformly decreasing, or if zerovalued denominator warnings are being issued. The step size is too small if the objective is changing very slowly. Setting the termination condition can be done easily once a good step size parameter is found; either increase the maximum iterations to a large number and allow SGD to find a minimum, or set the maximum iterations to 0 (allowing infinite iterations) and set the tolerance (specified by tolerance
) to define the maximum allowed difference between objectives for SGD to terminate. Be careful—setting the tolerance instead of the maximum iterations can take a very long time and may actually never converge due to the properties of the SGD optimizer. Note that a single iteration of SGD refers to a single point, so to take a single pass over the dataset, set the value of the max_iterations
parameter equal to the number of points in the dataset.
The LBFGS optimizer, specified by the value ‘lbfgs’ for the parameter optimizer
, uses a backtracking line search algorithm to minimize a function. The following parameters are used by LBFGS: num_basis
(specifies the number of memory points used by LBFGS), max_iterations
, armijo_constant
, wolfe
, tolerance
(the optimization is terminated when the gradient norm is below this value), max_line_search_trials
, min_step
, and max_step
(which both refer to the line search routine). For more details on the LBFGS optimizer, consult either the mlpack LBFGS documentation (in lbfgs.hpp) or the vast set of published literature on LBFGS.
By default, the SGD optimizer is used.
🔗 See also
 lmnn()
 Neighbourhood components analysis on Wikipedia
 Neighbourhood components analysis (pdf)
 NCA C++ class documentation
🔗 knn()
kNearestNeighbors Search
julia> using mlpack: knn
julia> distances, neighbors, output_model = knn( ;
algorithm="dual_tree", epsilon=0, input_model=nothing, k=0,
leaf_size=20, query=zeros(0, 0), random_basis=false,
reference=zeros(0, 0), rho=0.7, seed=0, tau=0, tree_type="kd",
true_distances=zeros(0, 0), true_neighbors=zeros(Int, 0, 0),
verbose=false)
An implementation of knearestneighbor search using singletree and dualtree algorithms. Given a set of reference points and query points, this can find the k nearest neighbors in the reference set of each query point using trees; trees that are built can be saved for future use. Detailed documentation.
🔗 Input options
name  type  description  default 

algorithm 
String 
Type of neighbor search: ‘naive’, ‘single_tree’, ‘dual_tree’, ‘greedy’.  "dual_tree" 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
epsilon 
Float64 
If specified, will do approximate nearest neighbor search with given relative error.  0 
input_model 
KNNModel 
Pretrained kNN model.  nothing 
k 
Int 
Number of nearest neighbors to find.  0 
leaf_size 
Int 
Leaf size for tree building (used for kdtrees, vp trees, random projection trees, UB trees, R trees, R* trees, X trees, Hilbert R trees, R+ trees, R++ trees, spill trees, and octrees).  20 
query 
Float64 matrixlike 
Matrix containing query points (optional).  zeros(0, 0) 
random_basis 
Bool 
Before treebuilding, project the data onto a random orthogonal basis.  false 
reference 
Float64 matrixlike 
Matrix containing the reference dataset.  zeros(0, 0) 
rho 
Float64 
Balance threshold (only valid for spill trees).  0.7 
seed 
Int 
Random seed (if 0, std::time(NULL) is used).  0 
tau 
Float64 
Overlapping size (only valid for spill trees).  0 
tree_type 
String 
Type of tree to use: ‘kd’, ‘vp’, ‘rp’, ‘maxrp’, ‘ub’, ‘cover’, ‘r’, ‘rstar’, ‘x’, ‘ball’, ‘hilbertr’, ‘rplus’, ‘rplusplus’, ‘spill’, ‘oct’.  "kd" 
true_distances 
Float64 matrixlike 
Matrix of true distances to compute the effective error (average relative error) (it is printed when v is specified).  zeros(0, 0) 
true_neighbors 
Int matrixlike 
Matrix of true neighbors to compute the recall (it is printed when v is specified).  zeros(Int, 0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

distances 
Float64 matrixlike 
Matrix to output distances into. 
neighbors 
Int matrixlike 
Matrix to output neighbors into. 
output_model 
KNNModel 
If specified, the kNN model will be output here. 
🔗 Detailed documentation
This program will calculate the knearestneighbors of a set of points using kdtrees or cover trees (cover tree support is experimental and may be slow). You may specify a separate set of reference points and query points, or just a reference set which will be used as both the reference and query set.
🔗 Example
For example, the following command will calculate the 5 nearest neighbors of each point in input
and store the distances in distances
and the neighbors in neighbors
:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> distances, neighbors, _ = knn(k=5, reference=input)
The output is organized such that row i and column j in the neighbors output matrix corresponds to the index of the point in the reference set which is the j’th nearest neighbor from the point in the query set with index i. Row j and column i in the distances output matrix corresponds to the distance between those two points.
🔗 See also
 lsh()
 krann()
 kfn()
 Treeindependent dualtree algorithms (pdf)
 NeighborSearch C++ class documentation
🔗 kfn()
kFurthestNeighbors Search
julia> using mlpack: kfn
julia> distances, neighbors, output_model = kfn( ;
algorithm="dual_tree", epsilon=0, input_model=nothing, k=0,
leaf_size=20, percentage=1, query=zeros(0, 0), random_basis=false,
reference=zeros(0, 0), seed=0, tree_type="kd", true_distances=zeros(0,
0), true_neighbors=zeros(Int, 0, 0), verbose=false)
An implementation of kfurthestneighbor search using singletree and dualtree algorithms. Given a set of reference points and query points, this can find the k furthest neighbors in the reference set of each query point using trees; trees that are built can be saved for future use. Detailed documentation.
🔗 Input options
name  type  description  default 

algorithm 
String 
Type of neighbor search: ‘naive’, ‘single_tree’, ‘dual_tree’, ‘greedy’.  "dual_tree" 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
epsilon 
Float64 
If specified, will do approximate furthest neighbor search with given relative error. Must be in the range [0,1).  0 
input_model 
KFNModel 
Pretrained kFN model.  nothing 
k 
Int 
Number of furthest neighbors to find.  0 
leaf_size 
Int 
Leaf size for tree building (used for kdtrees, vp trees, random projection trees, UB trees, R trees, R* trees, X trees, Hilbert R trees, R+ trees, R++ trees, and octrees).  20 
percentage 
Float64 
If specified, will do approximate furthest neighbor search. Must be in the range (0,1] (decimal form). Resultant neighbors will be at least (p*100) % of the distance as the true furthest neighbor.  1 
query 
Float64 matrixlike 
Matrix containing query points (optional).  zeros(0, 0) 
random_basis 
Bool 
Before treebuilding, project the data onto a random orthogonal basis.  false 
reference 
Float64 matrixlike 
Matrix containing the reference dataset.  zeros(0, 0) 
seed 
Int 
Random seed (if 0, std::time(NULL) is used).  0 
tree_type 
String 
Type of tree to use: ‘kd’, ‘vp’, ‘rp’, ‘maxrp’, ‘ub’, ‘cover’, ‘r’, ‘rstar’, ‘x’, ‘ball’, ‘hilbertr’, ‘rplus’, ‘rplusplus’, ‘oct’.  "kd" 
true_distances 
Float64 matrixlike 
Matrix of true distances to compute the effective error (average relative error) (it is printed when v is specified).  zeros(0, 0) 
true_neighbors 
Int matrixlike 
Matrix of true neighbors to compute the recall (it is printed when v is specified).  zeros(Int, 0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

distances 
Float64 matrixlike 
Matrix to output distances into. 
neighbors 
Int matrixlike 
Matrix to output neighbors into. 
output_model 
KFNModel 
If specified, the kFN model will be output here. 
🔗 Detailed documentation
This program will calculate the kfurthestneighbors of a set of points. You may specify a separate set of reference points and query points, or just a reference set which will be used as both the reference and query set.
🔗 Example
For example, the following will calculate the 5 furthest neighbors of eachpoint in input
and store the distances in distances
and the neighbors in neighbors
:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> distances, neighbors, _ = kfn(k=5, reference=input)
The output files are organized such that row i and column j in the neighbors output matrix corresponds to the index of the point in the reference set which is the j’th furthest neighbor from the point in the query set with index i. Row i and column j in the distances output file corresponds to the distance between those two points.
🔗 See also
 approx_kfn()
 knn()
 Treeindependent dualtree algorithms (pdf)
 NeighborSearch C++ class documentation
🔗 nmf()
Nonnegative Matrix Factorization
julia> using mlpack: nmf
julia> h, w = nmf(input, rank; initial_h=zeros(0, 0),
initial_w=zeros(0, 0), max_iterations=10000,
min_residue=1e05, seed=0, update_rules="multdist",
verbose=false)
An implementation of nonnegative matrix factorization. This can be used to decompose an input dataset into two lowrank nonnegative components. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
initial_h 
Float64 matrixlike 
Initial H matrix.  zeros(0, 0) 
initial_w 
Float64 matrixlike 
Initial W matrix.  zeros(0, 0) 
input 
Float64 matrixlike 
Input dataset to perform NMF on.  **** 
max_iterations 
Int 
Number of iterations before NMF terminates (0 runs until convergence.  10000 
min_residue 
Float64 
The minimum root mean square residue allowed for each iteration, below which the program terminates.  1e05 
rank 
Int 
Rank of the factorization.  **** 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
update_rules 
String 
Update rules for each iteration; ( multdist  multdiv  als ).  "multdist" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

h 
Float64 matrixlike 
Matrix to save the calculated H to. 
w 
Float64 matrixlike 
Matrix to save the calculated W to. 
🔗 Detailed documentation
This program performs nonnegative matrix factorization on the given dataset, storing the resulting decomposed matrices in the specified files. For an input dataset V, NMF decomposes V into two matrices W and H such that
V = W * H
where all elements in W and H are nonnegative. If V is of size (n x m), then W will be of size (n x r) and H will be of size (r x m), where r is the rank of the factorization (specified by the rank
parameter).
Optionally, the desired update rules for each NMF iteration can be chosen from the following list:
 multdist: multiplicative distancebased update rules (Lee and Seung 1999)
 multdiv: multiplicative divergencebased update rules (Lee and Seung 1999)
 als: alternating least squares update rules (Paatero and Tapper 1994)
The maximum number of iterations is specified with max_iterations
, and the minimum residue required for algorithm termination is specified with the min_residue
parameter.
🔗 Example
For example, to run NMF on the input matrix V
using the ‘multdist’ update rules with a rank10 decomposition and storing the decomposed matrices into W
and H
, the following command could be used:
julia> using CSV
julia> V = CSV.read("V.csv")
julia> H, W = nmf(V, 10; update_rules="multdist")
🔗 See also
 cf()
 Nonnegative matrix factorization on Wikipedia
 Algorithms for nonnegative matrix factorization (pdf)
 AMF C++ class documentation
🔗 pca()
Principal Components Analysis
julia> using mlpack: pca
julia> output = pca(input; decomposition_method="exact",
new_dimensionality=0, scale=false, var_to_retain=0,
verbose=false)
An implementation of several strategies for principal components analysis (PCA), a common preprocessing step. Given a dataset and a desired new dimensionality, this can reduce the dimensionality of the data using the linear transformation determined by PCA. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
decomposition_method 
String 
Method used for the principal components analysis: ‘exact’, ‘randomized’, ‘randomizedblockkrylov’, ‘quic’.  "exact" 
input 
Float64 matrixlike 
Input dataset to perform PCA on.  **** 
new_dimensionality 
Int 
Desired dimensionality of output dataset. If 0, no dimensionality reduction is performed.  0 
scale 
Bool 
If set, the data will be scaled before running PCA, such that the variance of each feature is 1.  false 
var_to_retain 
Float64 
Amount of variance to retain; should be between 0 and 1. If 1, all variance is retained. Overrides d.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save modified dataset to. 
🔗 Detailed documentation
This program performs principal components analysis on the given dataset using the exact, randomized, randomized block Krylov, or QUIC SVD method. It will transform the data onto its principal components, optionally performing dimensionality reduction by ignoring the principal components with the smallest eigenvalues.
Use the input
parameter to specify the dataset to perform PCA on. A desired new dimensionality can be specified with the new_dimensionality
parameter, or the desired variance to retain can be specified with the var_to_retain
parameter. If desired, the dataset can be scaled before running PCA with the scale
parameter.
Multiple different decomposition techniques can be used. The method to use can be specified with the decomposition_method
parameter, and it may take the values ‘exact’, ‘randomized’, or ‘quic’.
🔗 Example
For example, to reduce the dimensionality of the matrix data
to 5 dimensions using randomized SVD for the decomposition, storing the output matrix to data_mod
, the following command can be used:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> data_mod = pca(data; decomposition_method="randomized",
new_dimensionality=5)
🔗 See also
🔗 perceptron()
Perceptron
julia> using mlpack: perceptron
julia> output, output_model, predictions = perceptron( ;
input_model=nothing, labels=Int[], max_iterations=1000, test=zeros(0,
0), training=zeros(0, 0), verbose=false)
An implementation of a perceptron—a single level neural network–=for classification. Given labeled data, a perceptron can be trained and saved for future use; or, a pretrained perceptron can be used for classification on new points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
PerceptronModel 
Input perceptron model.  nothing 
labels 
Int vectorlike 
A matrix containing labels for the training set.  Int[] 
max_iterations 
Int 
The maximum number of iterations the perceptron is to be run  1000 
test 
Float64 matrixlike 
A matrix containing the test set.  zeros(0, 0) 
training 
Float64 matrixlike 
A matrix containing the training set.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Int vectorlike 
The matrix in which the predicted labels for the test set will be written. 
output_model 
PerceptronModel 
Output for trained perceptron model. 
predictions 
Int vectorlike 
The matrix in which the predicted labels for the test set will be written. 
🔗 Detailed documentation
This program implements a perceptron, which is a single level neural network. The perceptron makes its predictions based on a linear predictor function combining a set of weights with the feature vector. The perceptron learning rule is able to converge, given enough iterations (specified using the max_iterations
parameter), if the data supplied is linearly separable. The perceptron is parameterized by a matrix of weight vectors that denote the numerical weights of the neural network.
This program allows loading a perceptron from a model (via the input_model
parameter) or training a perceptron given training data (via the training
parameter), or both those things at once. In addition, this program allows classification on a test dataset (via the test
parameter) and the classification results on the test set may be saved with the predictions
output parameter. The perceptron model may be saved with the output_model
output parameter.
Note: the following parameter is deprecated and will be removed in mlpack 4.0.0: output
.
Use predictions
instead of output
.
🔗 Example
The training data given with the training
option may have class labels as its last dimension (so, if the training data is in CSV format, labels should be the last column). Alternately, the labels
parameter may be used to specify a separate matrix of labels.
All these options make it easy to train a perceptron, and then reuse that perceptron for later classification. The invocation below trains a perceptron on training_data
with labels training_labels
, and saves the model to perceptron_model
.
julia> using CSV
julia> training_data = CSV.read("training_data.csv")
julia> training_labels = CSV.read("training_labels.csv"; type=Int)
julia> _, perceptron_model, _ = perceptron(labels=training_labels,
training=training_data)
Then, this model can be reused for classification on the test data test_data
. The example below does precisely that, saving the predicted classes to predictions
.
julia> using CSV
julia> test_data = CSV.read("test_data.csv")
julia> _, _, predictions = perceptron(input_model=perceptron_model,
test=test_data)
Note that all of the options may be specified at once: predictions may be calculated right after training a model, and model training can occur even if an existing perceptron model is passed with the input_model
parameter. However, note that the number of classes and the dimensionality of all data must match. So you cannot pass a perceptron model trained on 2 classes and then retrain with a 4class dataset. Similarly, attempting classification on a 3dimensional dataset with a perceptron that has been trained on 8 dimensions will cause an error.
🔗 See also
🔗 preprocess_split()
Split Data
julia> using mlpack: preprocess_split
julia> test, test_labels, training, training_labels =
preprocess_split(input; input_labels=zeros(Int, 0, 0),
no_shuffle=false, seed=0, stratify_data=false, test_ratio=0.2,
verbose=false)
A utility to split data into a training and testing dataset. This can also split labels according to the same split. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Matrix containing data.  **** 
input_labels 
Int matrixlike 
Matrix containing labels.  zeros(Int, 0, 0) 
no_shuffle 
Bool 
Avoid shuffling the data before splitting.  false 
seed 
Int 
Random seed (0 for std::time(NULL)).  0 
stratify_data 
Bool 
Stratify the data according to labels  false 
test_ratio 
Float64 
Ratio of test set; if not set,the ratio defaults to 0.2  0.2 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

test 
Float64 matrixlike 
Matrix to save test data to. 
test_labels 
Int matrixlike 
Matrix to save test labels to. 
training 
Float64 matrixlike 
Matrix to save training data to. 
training_labels 
Int matrixlike 
Matrix to save train labels to. 
🔗 Detailed documentation
This utility takes a dataset and optionally labels and splits them into a training set and a test set. Before the split, the points in the dataset are randomly reordered. The percentage of the dataset to be used as the test set can be specified with the test_ratio
parameter; the default is 0.2 (20%).
The output training and test matrices may be saved with the training
and test
output parameters.
Optionally, labels can also be split along with the data by specifying the input_labels
parameter. Splitting labels works the same way as splitting the data. The output training and test labels may be saved with the training_labels
and test_labels
output parameters, respectively.
🔗 Example
So, a simple example where we want to split the dataset X
into X_train
and X_test
with 60% of the data in the training set and 40% of the dataset in the test set, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_test, _, X_train, _ = preprocess_split(X; test_ratio=0.4)
Also by default the dataset is shuffled and split; you can provide the no_shuffle
option to avoid shuffling the data; an example to avoid shuffling of data is:
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_test, _, X_train, _ = preprocess_split(X; no_shuffle=1,
test_ratio=0.4)
If we had a dataset X
and associated labels y
, and we wanted to split these into X_train
, y_train
, X_test
, and y_test
, with 30% of the data in the test set, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> y = CSV.read("y.csv"; type=Int)
julia> X_test, y_test, X_train, y_train = preprocess_split(X;
input_labels=y, test_ratio=0.3)
To maintain the ratio of each class in the train and test sets, thestratify_data
option can be used.
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_test, _, X_train, _ = preprocess_split(X; stratify_data=1,
test_ratio=0.4)
🔗 See also
🔗 preprocess_binarize()
Binarize Data
julia> using mlpack: preprocess_binarize
julia> output = preprocess_binarize(input; dimension=0, threshold=0,
verbose=false)
A utility to binarize a dataset. Given a dataset, this utility converts each value in the desired dimension(s) to 0 or 1; this can be a useful preprocessing step. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
dimension 
Int 
Dimension to apply the binarization. If not set, the program will binarize every dimension by default.  0 
input 
Float64 matrixlike 
Input data matrix.  **** 
threshold 
Float64 
Threshold to be applied for binarization. If not set, the threshold defaults to 0.0.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix in which to save the output. 
🔗 Detailed documentation
This utility takes a dataset and binarizes the variables into either 0 or 1 given threshold. User can apply binarization on a dimension or the whole dataset. The dimension to apply binarization to can be specified using the dimension
parameter; if left unspecified, every dimension will be binarized. The threshold for binarization can also be specified with the threshold
parameter; the default threshold is 0.0.
The binarized matrix may be saved with the output
output parameter.
🔗 Example
For example, if we want to set all variables greater than 5 in the dataset X
to 1 and variables less than or equal to 5.0 to 0, and save the result to Y
, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> Y = preprocess_binarize(X; threshold=5)
But if we want to apply this to only the first (0th) dimension of X
, we could instead run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> Y = preprocess_binarize(X; dimension=0, threshold=5)
🔗 See also
🔗 preprocess_describe()
Descriptive Statistics
julia> using mlpack: preprocess_describe
julia> preprocess_describe(input; dimension=0,
population=false, precision=4, row_major=false,
verbose=false, width=8)
A utility for printing descriptive statistics about a dataset. This prints a number of details about a dataset in a tabular format. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
dimension 
Int 
Dimension of the data. Use this to specify a dimension  0 
input 
Float64 matrixlike 
Matrix containing data,  **** 
population 
Bool 
If specified, the program will calculate statistics assuming the dataset is the population. By default, the program will assume the dataset as a sample.  false 
precision 
Int 
Precision of the output statistics.  4 
row_major 
Bool 
If specified, the program will calculate statistics across rows, not across columns. (Remember that in mlpack, a column represents a point, so this option is generally not necessary.)  false 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
width 
Int 
Width of the output table.  8 
🔗 Detailed documentation
This utility takes a dataset and prints out the descriptive statistics of the data. Descriptive statistics is the discipline of quantitatively describing the main features of a collection of information, or the quantitative description itself. The program does not modify the original file, but instead prints out the statistics to the console. The printed result will look like a table.
Optionally, width and precision of the output can be adjusted by a user using the width
and precision
parameters. A user can also select a specific dimension to analyze if there are too many dimensions. The population
parameter can be specified when the dataset should be considered as a population. Otherwise, the dataset will be considered as a sample.
🔗 Example
So, a simple example where we want to print out statistical facts about the dataset X
using the default settings, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> preprocess_describe(X; verbose=1)
If we want to customize the width to 10 and precision to 5 and consider the dataset as a population, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> preprocess_describe(X; precision=5, verbose=1, width=10)
🔗 See also
🔗 preprocess_scale()
Scale Data
julia> using mlpack: preprocess_scale
julia> output, output_model = preprocess_scale(input; epsilon=1e06,
input_model=nothing, inverse_scaling=false, max_value=1, min_value=0,
scaler_method="standard_scaler", seed=0, verbose=false)
A utility to perform feature scaling on datasets using one of sixtechniques. Both scaling and inverse scaling are supported, andscalers can be saved and then applied to other datasets. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
epsilon 
Float64 
regularization Parameter for pcawhitening, or zcawhitening, should be between 1 to 1.  1e06 
input 
Float64 matrixlike 
Matrix containing data.  **** 
input_model 
ScalingModel 
Input Scaling model.  nothing 
inverse_scaling 
Bool 
Inverse Scaling to get original dataset  false 
max_value 
Int 
Ending value of range for min_max_scaler.  1 
min_value 
Int 
Starting value of range for min_max_scaler.  0 
scaler_method 
String 
method to use for scaling, the default is standard_scaler.  "standard_scaler" 
seed 
Int 
Random seed (0 for std::time(NULL)).  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save scaled data to. 
output_model 
ScalingModel 
Output scaling model. 
🔗 Detailed documentation
This utility takes a dataset and performs feature scaling using one of the six scaler methods namely: ‘max_abs_scaler’, ‘mean_normalization’, ‘min_max_scaler’ ,’standard_scaler’, ‘pca_whitening’ and ‘zca_whitening’. The function takes a matrix as input
and a scaling method type which you can specify using scaler_method
parameter; the default is standard scaler, and outputs a matrix with scaled feature.
The output scaled feature matrix may be saved with the output
output parameters.
The model to scale features can be saved using output_model
and later can be loaded back usinginput_model
.
🔗 Example
So, a simple example where we want to scale the dataset X
into X_scaled
with standard_scaler as scaler_method, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_scaled, _ = preprocess_scale(X;
scaler_method="standard_scaler")
A simple example where we want to whiten the dataset X
into X_whitened
with PCA as whitening_method and use 0.01 as regularization parameter, we could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_scaled, _ = preprocess_scale(X; epsilon=0.01,
scaler_method="pca_whitening")
You can also retransform the scaled dataset back usinginverse_scaling
. An example to rescale : X_scaled
into X
using the saved model input_model
is:
julia> using CSV
julia> X_scaled = CSV.read("X_scaled.csv")
julia> X, _ = preprocess_scale(X_scaled; input_model=saved,
inverse_scaling=1)
Another simple example where we want to scale the dataset X
into X_scaled
with min_max_scaler as scaler method, where scaling range is 1 to 3 instead of default 0 to 1. We could run
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_scaled, _ = preprocess_scale(X; max_value=3, min_value=1,
scaler_method="min_max_scaler")
🔗 See also
🔗 preprocess_one_hot_encoding()
One Hot Encoding
julia> using mlpack: preprocess_one_hot_encoding
julia> output = preprocess_one_hot_encoding(input; dimensions=[],
verbose=false)
A utility to do onehot encoding on features of dataset. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
dimensions 
Array{Int, 1} 
Index of dimensions that need to be onehot encoded (if unspecified, all categorical dimensions are onehot encoded).  [] 
input 
Tuple{Array{Bool, 1}, Array{Float64, 2}} 
Matrix containing data.  **** 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save onehot encoded features data to. 
🔗 Detailed documentation
This utility takes a dataset and a vector of indices and does onehot encoding of the respective features at those indices. Indices represent the IDs of the dimensions to be onehot encoded.
If no dimensions are specified with dimensions
, then all categoricaltype dimensions will be onehot encoded. Otherwise, only the dimensions given in dimensions
will be onehot encoded.
The output matrix with encoded features may be saved with the output
parameters.
🔗 Example
So, a simple example where we want to encode 1st and 3rd feature from dataset X
into X_output
would be
julia> using CSV
julia> X = CSV.read("X.csv")
julia> X_ouput = preprocess_one_hot_encoding(X; dimensions=1)
🔗 See also
🔗 radical()
RADICAL
julia> using mlpack: radical
julia> output_ic, output_unmixing = radical(input; angles=150,
noise_std_dev=0.175, objective=false, replicates=30, seed=0, sweeps=0,
verbose=false)
An implementation of RADICAL, a method for independent component analysis (ICA). Given a dataset, this can decompose the dataset into an unmixing matrix and an independent component matrix; this can be useful for preprocessing. Detailed documentation.
🔗 Input options
name  type  description  default 

angles 
Int 
Number of angles to consider in bruteforce search during Radical2D.  150 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input 
Float64 matrixlike 
Input dataset for ICA.  **** 
noise_std_dev 
Float64 
Standard deviation of Gaussian noise.  0.175 
objective 
Bool 
If set, an estimate of the final objective function is printed.  false 
replicates 
Int 
Number of Gaussianperturbed replicates to use (per point) in Radical2D.  30 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
sweeps 
Int 
Number of sweeps; each sweep calls Radical2D once for each pair of dimensions.  0 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_ic 
Float64 matrixlike 
Matrix to save independent components to. 
output_unmixing 
Float64 matrixlike 
Matrix to save unmixing matrix to. 
🔗 Detailed documentation
An implementation of RADICAL, a method for independent component analysis (ICA). Assuming that we have an input matrix X, the goal is to find a square unmixing matrix W such that Y = W * X and the dimensions of Y are independent components. If the algorithm is running particularly slowly, try reducing the number of replicates.
The input matrix to perform ICA on should be specified with the input
parameter. The output matrix Y may be saved with the output_ic
output parameter, and the output unmixing matrix W may be saved with the output_unmixing
output parameter.
🔗 Example
For example, to perform ICA on the matrix X
with 40 replicates, saving the independent components to ic
, the following command may be used:
julia> using CSV
julia> X = CSV.read("X.csv")
julia> ic, _ = radical(X; replicates=40)
🔗 See also
 Independent component analysis on Wikipedia
 ICA using spacings estimates of entropy (pdf)
 Radical C++ class documentation
🔗 random_forest()
Random forests
julia> using mlpack: random_forest
julia> output_model, predictions, probabilities = random_forest( ;
input_model=nothing, labels=Int[], maximum_depth=0,
minimum_gain_split=0, minimum_leaf_size=1, num_trees=10,
print_training_accuracy=false, seed=0, subspace_dim=0, test=zeros(0,
0), test_labels=Int[], training=zeros(0, 0), verbose=false,
warm_start=false)
An implementation of the standard random forest algorithm by Leo Breiman for classification. Given labeled data, a random forest can be trained and saved for future use; or, a pretrained random forest can be used for classification. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
RandomForestModel 
Pretrained random forest to use for classification.  nothing 
labels 
Int vectorlike 
Labels for training dataset.  Int[] 
maximum_depth 
Int 
Maximum depth of the tree (0 means no limit).  0 
minimum_gain_split 
Float64 
Minimum gain needed to make a split when building a tree.  0 
minimum_leaf_size 
Int 
Minimum number of points in each leaf node.  1 
num_trees 
Int 
Number of trees in the random forest.  10 
print_training_accuracy 
Bool 
If set, then the accuracy of the model on the training set will be predicted (verbose must also be specified).  false 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
subspace_dim 
Int 
Dimensionality of random subspace to use for each split. ‘0’ will autoselect the square root of data dimensionality.  0 
test 
Float64 matrixlike 
Test dataset to produce predictions for.  zeros(0, 0) 
test_labels 
Int vectorlike 
Test dataset labels, if accuracy calculation is desired.  Int[] 
training 
Float64 matrixlike 
Training dataset.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
warm_start 
Bool 
If true and passed along with training and input_model then trains more trees on top of existing model. 
false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
RandomForestModel 
Model to save trained random forest to. 
predictions 
Int vectorlike 
Predicted classes for each point in the test set. 
probabilities 
Float64 matrixlike 
Predicted class probabilities for each point in the test set. 
🔗 Detailed documentation
This program is an implementation of the standard random forest classification algorithm by Leo Breiman. A random forest can be trained and saved for later use, or a random forest may be loaded and predictions or class probabilities for points may be generated.
The training set and associated labels are specified with the training
and labels
parameters, respectively. The labels should be in the range [0, num_classes  1]
. Optionally, if labels
is not specified, the labels are assumed to be the last dimension of the training dataset.
When a model is trained, the output_model
output parameter may be used to save the trained model. A model may be loaded for predictions with the input_model
parameter. The input_model
parameter may not be specified when the training
parameter is specified. The minimum_leaf_size
parameter specifies the minimum number of training points that must fall into each leaf for it to be split. The num_trees
controls the number of trees in the random forest. The minimum_gain_split
parameter controls the minimum required gain for a decision tree node to split. Larger values will force higherconfidence splits. The maximum_depth
parameter specifies the maximum depth of the tree. The subspace_dim
parameter is used to control the number of random dimensions chosen for an individual node’s split. If print_training_accuracy
is specified, the calculated accuracy on the training set will be printed.
Test data may be specified with the test
parameter, and if performance measures are desired for that test set, labels for the test points may be specified with the test_labels
parameter. Predictions for each test point may be saved via the predictions
output parameter. Class probabilities for each prediction may be saved with the probabilities
output parameter.
🔗 Example
For example, to train a random forest with a minimum leaf size of 20 using 10 trees on the dataset contained in data
with labels labels
, saving the output random forest to rf_model
and printing the training error, one could call
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> rf_model, _, _ = random_forest(labels=labels,
minimum_leaf_size=20, num_trees=10, print_training_accuracy=1,
training=data)
Then, to use that model to classify points in test_set
and print the test error given the labels test_labels
using that model, while saving the predictions for each point to predictions
, one could call
julia> using CSV
julia> test_set = CSV.read("test_set.csv")
julia> test_labels = CSV.read("test_labels.csv"; type=Int)
julia> _, predictions, _ = random_forest(input_model=rf_model,
test=test_set, test_labels=test_labels)
🔗 See also
 decision_tree()
 hoeffding_tree()
 softmax_regression()
 Random forest on Wikipedia
 Random forests (pdf)
 RandomForest C++ class documentation
🔗 krann()
KRankApproximateNearestNeighbors (kRANN)
julia> using mlpack: krann
julia> distances, neighbors, output_model = krann( ; alpha=0.95,
first_leaf_exact=false, input_model=nothing, k=0, leaf_size=20,
naive=false, query=zeros(0, 0), random_basis=false, reference=zeros(0,
0), sample_at_leaves=false, seed=0, single_mode=false,
single_sample_limit=20, tau=5, tree_type="kd", verbose=false)
An implementation of rankapproximate knearestneighbor search (kRANN) using singletree and dualtree algorithms. Given a set of reference points and query points, this can find the k nearest neighbors in the reference set of each query point using trees; trees that are built can be saved for future use. Detailed documentation.
🔗 Input options
name  type  description  default 

alpha 
Float64 
The desired success probability.  0.95 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
first_leaf_exact 
Bool 
The flag to trigger sampling only after exactly exploring the first leaf.  false 
input_model 
RAModel 
Pretrained kNN model.  nothing 
k 
Int 
Number of nearest neighbors to find.  0 
leaf_size 
Int 
Leaf size for tree building (used for kdtrees, UB trees, R trees, R* trees, X trees, Hilbert R trees, R+ trees, R++ trees, and octrees).  20 
naive 
Bool 
If true, sampling will be done without using a tree.  false 
query 
Float64 matrixlike 
Matrix containing query points (optional).  zeros(0, 0) 
random_basis 
Bool 
Before treebuilding, project the data onto a random orthogonal basis.  false 
reference 
Float64 matrixlike 
Matrix containing the reference dataset.  zeros(0, 0) 
sample_at_leaves 
Bool 
The flag to trigger sampling at leaves.  false 
seed 
Int 
Random seed (if 0, std::time(NULL) is used).  0 
single_mode 
Bool 
If true, singletree search is used (as opposed to dualtree search.  false 
single_sample_limit 
Int 
The limit on the maximum number of samples (and hence the largest node you can approximate).  20 
tau 
Float64 
The allowed rankerror in terms of the percentile of the data.  5 
tree_type 
String 
Type of tree to use: ‘kd’, ‘ub’, ‘cover’, ‘r’, ‘x’, ‘rstar’, ‘hilbertr’, ‘rplus’, ‘rplusplus’, ‘oct’.  "kd" 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

distances 
Float64 matrixlike 
Matrix to output distances into. 
neighbors 
Int matrixlike 
Matrix to output neighbors into. 
output_model 
RAModel 
If specified, the kNN model will be output here. 
🔗 Detailed documentation
This program will calculate the k rankapproximatenearestneighbors of a set of points. You may specify a separate set of reference points and query points, or just a reference set which will be used as both the reference and query set. You must specify the rank approximation (in %) (and optionally the success probability).
🔗 Example
For example, the following will return 5 neighbors from the top 0.1% of the data (with probability 0.95) for each point in input
and store the distances in distances
and the neighbors in neighbors.csv
:
julia> using CSV
julia> input = CSV.read("input.csv")
julia> distances, neighbors, _ = krann(k=5, reference=input,
tau=0.1)
Note that tau must be set such that the number of points in the corresponding percentile of the data is greater than k. Thus, if we choose tau = 0.1 with a dataset of 1000 points and k = 5, then we are attempting to choose 5 nearest neighbors out of the closest 1 point – this is invalid and the program will terminate with an error message.
The output matrices are organized such that row i and column j in the neighbors output file corresponds to the index of the point in the reference set which is the i’th nearest neighbor from the point in the query set with index j. Row i and column j in the distances output file corresponds to the distance between those two points.
🔗 See also
 knn()
 lsh()
 Rankapproximate nearest neighbor search: Retaining meaning and speed in high dimensions (pdf)
 RASearch C++ class documentation
🔗 softmax_regression()
Softmax Regression
julia> using mlpack: softmax_regression
julia> output_model, predictions, probabilities = softmax_regression(
; input_model=nothing, labels=Int[], lambda=0.0001,
max_iterations=400, no_intercept=false, number_of_classes=0,
test=zeros(0, 0), test_labels=Int[], training=zeros(0, 0),
verbose=false)
An implementation of softmax regression for classification, which is a multiclass generalization of logistic regression. Given labeled data, a softmax regression model can be trained and saved for future use, or, a pretrained softmax regression model can be used for classification of new points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
SoftmaxRegression 
File containing existing model (parameters).  nothing 
labels 
Int vectorlike 
A matrix containing labels (0 or 1) for the points in the training set (y). The labels must order as a row.  Int[] 
lambda 
Float64 
L2regularization constant  0.0001 
max_iterations 
Int 
Maximum number of iterations before termination.  400 
no_intercept 
Bool 
Do not add the intercept term to the model.  false 
number_of_classes 
Int 
Number of classes for classification; if unspecified (or 0), the number of classes found in the labels will be used.  0 
test 
Float64 matrixlike 
Matrix containing test dataset.  zeros(0, 0) 
test_labels 
Int vectorlike 
Matrix containing test labels.  Int[] 
training 
Float64 matrixlike 
A matrix containing the training set (the matrix of predictors, X).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
SoftmaxRegression 
File to save trained softmax regression model to. 
predictions 
Int vectorlike 
Matrix to save predictions for test dataset into. 
probabilities 
Float64 matrixlike 
Matrix to save class probabilities for test dataset into. 
🔗 Detailed documentation
This program performs softmax regression, a generalization of logistic regression to the multiclass case, and has support for L2 regularization. The program is able to train a model, load an existing model, and give predictions (and optionally their accuracy) for test data.
Training a softmax regression model is done by giving a file of training points with the training
parameter and their corresponding labels with the labels
parameter. The number of classes can be manually specified with the number_of_classes
parameter, and the maximum number of iterations of the LBFGS optimizer can be specified with the max_iterations
parameter. The L2 regularization constant can be specified with the lambda
parameter and if an intercept term is not desired in the model, the no_intercept
parameter can be specified.
The trained model can be saved with the output_model
output parameter. If training is not desired, but only testing is, a model can be loaded with the input_model
parameter. At the current time, a loaded model cannot be trained further, so specifying both input_model
and training
is not allowed.
The program is also able to evaluate a model on test data. A test dataset can be specified with the test
parameter. Class predictions can be saved with the predictions
output parameter. If labels are specified for the test data with the test_labels
parameter, then the program will print the accuracy of the predictions on the given test set and its corresponding labels.
🔗 Example
For example, to train a softmax regression model on the data dataset
with labels labels
with a maximum of 1000 iterations for training, saving the trained model to sr_model
, the following command can be used:
julia> using CSV
julia> dataset = CSV.read("dataset.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> sr_model, _, _ = softmax_regression(labels=labels,
training=dataset)
Then, to use sr_model
to classify the test points in test_points
, saving the output predictions to predictions
, the following command can be used:
julia> using CSV
julia> test_points = CSV.read("test_points.csv")
julia> _, predictions, _ = softmax_regression(input_model=sr_model,
test=test_points)
🔗 See also
 logistic_regression()
 random_forest()
 Multinomial logistic regression (softmax regression) on Wikipedia
 SoftmaxRegression C++ class documentation
🔗 sparse_coding()
Sparse Coding
julia> using mlpack: sparse_coding
julia> codes, dictionary, output_model = sparse_coding( ; atoms=15,
initial_dictionary=zeros(0, 0), input_model=nothing, lambda1=0,
lambda2=0, max_iterations=0, newton_tolerance=1e06, normalize=false,
objective_tolerance=0.01, seed=0, test=zeros(0, 0), training=zeros(0,
0), verbose=false)
An implementation of Sparse Coding with Dictionary Learning. Given a dataset, this will decompose the dataset into a sparse combination of a few dictionary elements, where the dictionary is learned during computation; a dictionary can be reused for future sparse coding of new points. Detailed documentation.
🔗 Input options
name  type  description  default 

atoms 
Int 
Number of atoms in the dictionary.  15 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
initial_dictionary 
Float64 matrixlike 
Optional initial dictionary matrix.  zeros(0, 0) 
input_model 
SparseCoding 
File containing input sparse coding model.  nothing 
lambda1 
Float64 
Sparse coding l1norm regularization parameter.  0 
lambda2 
Float64 
Sparse coding l2norm regularization parameter.  0 
max_iterations 
Int 
Maximum number of iterations for sparse coding (0 indicates no limit).  0 
newton_tolerance 
Float64 
Tolerance for convergence of Newton method.  1e06 
normalize 
Bool 
If set, the input data matrix will be normalized before coding.  false 
objective_tolerance 
Float64 
Tolerance for convergence of the objective function.  0.01 
seed 
Int 
Random seed. If 0, ‘std::time(NULL)’ is used.  0 
test 
Float64 matrixlike 
Optional matrix to be encoded by trained model.  zeros(0, 0) 
training 
Float64 matrixlike 
Matrix of training data (X).  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

codes 
Float64 matrixlike 
Matrix to save the output sparse codes of the test matrix (–test_file) to. 
dictionary 
Float64 matrixlike 
Matrix to save the output dictionary to. 
output_model 
SparseCoding 
File to save trained sparse coding model to. 
🔗 Detailed documentation
An implementation of Sparse Coding with Dictionary Learning, which achieves sparsity via an l1norm regularizer on the codes (LASSO) or an (l1+l2)norm regularizer on the codes (the Elastic Net). Given a dense data matrix X with d dimensions and n points, sparse coding seeks to find a dense dictionary matrix D with k atoms in d dimensions, and a sparse coding matrix Z with n points in k dimensions.
The original data matrix X can then be reconstructed as Z * D. Therefore, this program finds a representation of each point in X as a sparse linear combination of atoms in the dictionary D.
The sparse coding is found with an algorithm which alternates between a dictionary step, which updates the dictionary D, and a sparse coding step, which updates the sparse coding matrix.
Once a dictionary D is found, the sparse coding model may be used to encode other matrices, and saved for future usage.
To run this program, either an input matrix or an alreadysaved sparse coding model must be specified. An input matrix may be specified with the training
option, along with the number of atoms in the dictionary (specified with the atoms
parameter). It is also possible to specify an initial dictionary for the optimization, with the initial_dictionary
parameter. An input model may be specified with the input_model
parameter.
🔗 Example
As an example, to build a sparse coding model on the dataset data
using 200 atoms and an l1regularization parameter of 0.1, saving the model into model
, use
julia> using CSV
julia> data = CSV.read("data.csv")
julia> _, _, model = sparse_coding(atoms=200, lambda1=0.1,
training=data)
Then, this model could be used to encode a new matrix, otherdata
, and save the output codes to codes
:
julia> using CSV
julia> otherdata = CSV.read("otherdata.csv")
julia> codes, _, _ = sparse_coding(input_model=model,
test=otherdata)
🔗 See also
 local_coordinate_coding()
 Sparse dictionary learning on Wikipedia
 Efficient sparse coding algorithms (pdf)
 Regularization and variable selection via the elastic net
 SparseCoding C++ class documentation
🔗 adaboost()
AdaBoost
julia> using mlpack: adaboost
julia> output, output_model, predictions, probabilities = adaboost( ;
input_model=nothing, iterations=1000, labels=Int[], test=zeros(0, 0),
tolerance=1e10, training=zeros(0, 0), verbose=false,
weak_learner="decision_stump")
An implementation of the AdaBoost.MH (Adaptive Boosting) algorithm for classification. This can be used to train an AdaBoost model on labeled data or use an existing AdaBoost model to predict the classes of new points. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
AdaBoostModel 
Input AdaBoost model.  nothing 
iterations 
Int 
The maximum number of boosting iterations to be run (0 will run until convergence.)  1000 
labels 
Int vectorlike 
Labels for the training set.  Int[] 
test 
Float64 matrixlike 
Test dataset.  zeros(0, 0) 
tolerance 
Float64 
The tolerance for change in values of the weighted error during training.  1e10 
training 
Float64 matrixlike 
Dataset for training AdaBoost.  zeros(0, 0) 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
weak_learner 
String 
The type of weak learner to use: ‘decision_stump’, or ‘perceptron’.  "decision_stump" 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Int vectorlike 
Predicted labels for the test set. 
output_model 
AdaBoostModel 
Output trained AdaBoost model. 
predictions 
Int vectorlike 
Predicted labels for the test set. 
probabilities 
Float64 matrixlike 
Predicted class probabilities for each point in the test set. 
🔗 Detailed documentation
This program implements the AdaBoost (or Adaptive Boosting) algorithm. The variant of AdaBoost implemented here is AdaBoost.MH. It uses a weak learner, either decision stumps or perceptrons, and over many iterations, creates a strong learner that is a weighted ensemble of weak learners. It runs these iterations until a tolerance value is crossed for change in the value of the weighted training error.
For more information about the algorithm, see the paper “Improved Boosting Algorithms Using ConfidenceRated Predictions”, by R.E. Schapire and Y. Singer.
This program allows training of an AdaBoost model, and then application of that model to a test dataset. To train a model, a dataset must be passed with the training
option. Labels can be given with the labels
option; if no labels are specified, the labels will be assumed to be the last column of the input dataset. Alternately, an AdaBoost model may be loaded with the input_model
option.
Once a model is trained or loaded, it may be used to provide class predictions for a given test dataset. A test dataset may be specified with the test
parameter. The predicted classes for each point in the test dataset are output to the predictions
output parameter. The AdaBoost model itself is output to the output_model
output parameter.
Note: the following parameter is deprecated and will be removed in mlpack 4.0.0: output
.
Use predictions
instead of output
.
🔗 Example
For example, to run AdaBoost on an input dataset data
with labels labels
and perceptrons as the weak learner type, storing the trained model in model
, one could use the following command:
julia> using CSV
julia> data = CSV.read("data.csv")
julia> labels = CSV.read("labels.csv"; type=Int)
julia> _, model, _, _ = adaboost(labels=labels, training=data,
weak_learner="perceptron")
Similarly, an alreadytrained model in model
can be used to provide class predictions from test data test_data
and store the output in predictions
with the following command:
julia> using CSV
julia> test_data = CSV.read("test_data.csv")
julia> _, _, predictions, _ = adaboost(input_model=model,
test=test_data)
🔗 See also
 AdaBoost on Wikipedia
 Improved boosting algorithms using confidencerated predictions (pdf)
 Perceptron
 Decision Trees
 AdaBoost C++ class documentation
🔗 linear_regression()
Simple Linear Regression and Prediction
julia> using mlpack: linear_regression
julia> output_model, output_predictions = linear_regression( ;
input_model=nothing, lambda=0, test=zeros(0, 0), training=zeros(0, 0),
training_responses=Float64[], verbose=false)
An implementation of simple linear regression and ridge regression using ordinary least squares. Given a dataset and responses, a model can be trained and saved for later use, or a pretrained model can be used to output regression predictions for a test set. Detailed documentation.
🔗 Input options
name  type  description  default 

check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
input_model 
LinearRegression 
Existing LinearRegression model to use.  nothing 
lambda 
Float64 
Tikhonov regularization for ridge regression. If 0, the method reduces to linear regression.  0 
test 
Float64 matrixlike 
Matrix containing X’ (test regressors).  zeros(0, 0) 
training 
Float64 matrixlike 
Matrix containing training set X (regressors).  zeros(0, 0) 
training_responses 
Float64 vectorlike 
Optional vector containing y (responses). If not given, the responses are assumed to be the last row of the input file.  Float64[] 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output_model 
LinearRegression 
Output LinearRegression model. 
output_predictions 
Float64 vectorlike 
If –test_file is specified, this matrix is where the predicted responses will be saved. 
🔗 Detailed documentation
An implementation of simple linear regression and simple ridge regression using ordinary least squares. This solves the problem
y = X * b + e
where X (specified by training
) and y (specified either as the last column of the input matrix training
or via the training_responses
parameter) are known and b is the desired variable. If the covariance matrix (X’X) is not invertible, or if the solution is overdetermined, then specify a Tikhonov regularization constant (with lambda
) greater than 0, which will regularize the covariance matrix to make it invertible. The calculated b may be saved with the output_predictions
output parameter.
Optionally, the calculated value of b is used to predict the responses for another matrix X’ (specified by the test
parameter):
y’ = X’ * b
and the predicted responses y’ may be saved with the output_predictions
output parameter. This type of regression is related to leastangle regression, which mlpack implements as the ‘lars’ program.
🔗 Example
For example, to run a linear regression on the dataset X
with responses y
, saving the trained model to lr_model
, the following command could be used:
julia> using CSV
julia> X = CSV.read("X.csv")
julia> y = CSV.read("y.csv")
julia> lr_model, _ = linear_regression(training=X,
training_responses=y)
Then, to use lr_model
to predict responses for a test set X_test
, saving the predictions to X_test_responses
, the following command could be used:
julia> using CSV
julia> X_test = CSV.read("X_test.csv")
julia> _, X_test_responses = linear_regression(input_model=lr_model,
test=X_test)
🔗 See also
🔗 image_converter()
Image Converter
julia> using mlpack: image_converter
julia> output = image_converter(input;
channels=0, dataset=zeros(0, 0), height=0,
quality=90, save=false, verbose=false, width=0)
A utility to load an image or set of images into a single dataset that can then be used by other mlpack methods and utilities. This can also unpack an image dataset into individual files, for instance after mlpack methods have been used. Detailed documentation.
🔗 Input options
name  type  description  default 

channels 
Int 
Number of channels in the image.  0 
check_input_matrices 
Bool 
If specified, the input matrix is checked for NaN and inf values; an exception is thrown if any are found.  false 
dataset 
Float64 matrixlike 
Input matrix to save as images.  zeros(0, 0) 
height 
Int 
Height of the images.  0 
input 
Array{String, 1} 
Image filenames which have to be loaded/saved.  **** 
quality 
Int 
Compression of the image if saved as jpg (0100).  90 
save 
Bool 
Save a dataset as images.  false 
verbose 
Bool 
Display informational messages and the full list of parameters and timers at the end of execution.  false 
width 
Int 
Width of the image.  0 
🔗 Output options
Results are returned as a tuple, and can be unpacked directly into return values or stored directly as a tuple; undesired results can be ignored with the _ keyword.
name  type  description 

output 
Float64 matrixlike 
Matrix to save images data to, Onlyneeded if you are specifying ‘save’ option. 
🔗 Detailed documentation
This utility takes an image or an array of images and loads them to a matrix. You can optionally specify the height height
width width
and channel channels
of the images that needs to be loaded; otherwise, these parameters will be automatically detected from the image.
There are other options too, that can be specified such as quality
.
You can also provide a dataset and save them as images using dataset
and save
as an parameter.
🔗 Example
An example to load an image :
julia> Y = image_converter(X; channels=3, height=256, width=256)
An example to save an image is :
julia> using CSV
julia> Y = CSV.read("Y.csv")
julia> _ = image_converter(X; channels=3, dataset=Y, height=256,
save=1, width=256)