overview

High-quality documentation is a development goal of mlpack. mlpack’s documentation is split into two parts: documentation for the bindings, and documentation for the C++ library. Generally, working with the bindings is a good choice for simple machine learning and data science tasks, and writing C++ is a good idea when complex or custom functionality is desired.

All interfaces are heavily documented, and if you find a documentation issue, please report it.

quickstart

Just getting started with mlpack? Try these quickstart tutorials for the bindings to other languages.

Once you’re comfortable with the quickstart guides for the language of your choice, full documentation for every binding can be found below. Quick links are in the left sidebar.

• Binding documentation

The C++ interfaces of mlpack are carefully documented in the source code, which can be browsed for more details.

• Source code

A number of tutorials are available covering individual algorithms and functionality inside of mlpack, both for bindings to other languages and for the C++ interface.

• Tutorials

mlpack 4.1.0 binding documentation

data formats

mlpack bindings for CLI 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”).
• double: A floating-point number (i.e., “0.5”).
• flag: A boolean flag option. If not specified, it is false; if specified, it is true.
• string: A character string (i.e., “hello”).
• int vector: A vector of integers, separated by commas (i.e., “1,2,3”).
• string vector: A vector of strings, separated by commas (i.e., “hello”,”goodbye”).
• 2-d matrix file: A data matrix filename. The file can be CSV (.csv), TSV (.csv), ASCII (space-separated values, .txt), Armadillo ASCII (.txt), PGM (.pgm), PPM (.ppm), Armadillo binary (.bin), or HDF5 (.h5, .hdf, .hdf5, or .he5), if mlpack was compiled with HDF5 support. The type of the data is detected by the extension of the filename. The storage should be such that one row corresponds to one point, and one column corresponds to one dimension (this is the typical storage format for on-disk data). CSV files will be checked for a header; if no header is found, the first row will be loaded as a data point. All values of the matrix will be loaded as double-precision floating point data.
• 2-d index matrix file: A data matrix filename, where the matrix holds only non-negative integer values. This type is often used for labels or indices. The file can be CSV (.csv), TSV (.csv), ASCII (space-separated values, .txt), Armadillo ASCII (.txt), PGM (.pgm), PPM (.ppm), Armadillo binary (.bin), or HDF5 (.h5, .hdf, .hdf5, or .he5), if mlpack was compiled with HDF5 support. The type of the data is detected by the extension of the filename. The storage should be such that one row corresponds to one point, and one column corresponds to one dimension (this is the typical storage format for on-disk data). CSV files will be checked for a header; if no header is found, the first row will be loaded as a data point. All values of the matrix will be loaded as unsigned integers.
• 1-d matrix file: A one-dimensional vector filename. This file can take the same formats as the data matrix filenames; however, it must either contain one row and many columns, or one column and many rows.
• 1-d index matrix file: A one-dimensional vector filename, where the matrix holds only non-negative integer values. This type is typically used for labels or predictions or other indices. This file can take the same formats as the data matrix filenames; however, it must either contain one row and many columns, or one column and many rows.
• 2-d categorical matrix file: A filename for a data matrix that can contain categorical (non-numeric) data. If the file contains only numeric data, then the same formats for regular data matrices can be used. If the file contains strings or other values that can’t be parsed as numbers, then the type to be loaded must be CSV (.csv) or ARFF (.arff). Any non-numeric data will be converted to an unsigned integer value, and dimensions where the data is converted will be treated as categorical dimensions. When using this format, there is no need for one-hot encoding of categorical data.
• mlpackModel file: A filename containing an mlpack model. These can have one of three formats: binary (.bin), text (.txt), and XML (.xml). The XML format produces the largest (but most human-readable) files, while the binary format can be significantly more compact and quicker to load and save.

mlpack_approx_kfn

Approximate furthest neighbor search

$ mlpack_approx_kfn [--algorithm 'ds'] [--calculate_error]
        [--exact_distances_file <string>] [--help] [--info <string>]
        [--input_model_file <string>] [--k 0] [--num_projections 5]
        [--num_tables 5] [--query_file <string>] [--reference_file <string>]
        [--verbose] [--version] [--distances_file <string>] [--neighbors_file
        <string>] [--output_model_file <string>]

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

Output options

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 data-dependent 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_file (-r), specify a query set with --query_file (-q), and specify algorithm parameters with --num_tables (-t) and --num_projections (-p) (or don’t and defaults will be used). The algorithm to be used (either ‘ds’—the default—or ‘qdafn’) may be specified with --algorithm (-a). Also specify the number of neighbors to search for with --k (-k).

Note that for ‘qdafn’ in lower dimensions, --num_projections (-p) 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_file (-M) 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_file (-m) option.

Results for each query point can be stored with the --neighbors_file (-n) and --distances_file (-d) 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.csv' as the reference set and 'query_set.csv' as the query set using DrusillaSelect, storing the furthest neighbor indices to 'neighbors.csv' and the furthest neighbor distances to 'distances.csv', one could call

$ mlpack_approx_kfn --query_file query_set.csv --reference_file
  reference_set.csv --k 5 --algorithm ds --neighbors_file neighbors.csv
  --distances_file distances.csv

and to perform approximate all-furthest-neighbors search with k=1 on the set 'data.csv' storing only the furthest neighbor distances to 'distances.csv', one could call

$ mlpack_approx_kfn --reference_file reference_set.csv --k 1 --distances_file
  distances.csv

A trained model can be re-used. If a model has been previously saved to 'model.bin', then we may find 3 approximate furthest neighbors on a query set 'new_query_set.csv' using that model and store the furthest neighbor indices into 'neighbors.csv' by calling

$ mlpack_approx_kfn --input_model_file model.bin --query_file
  new_query_set.csv --k 3 --neighbors_file neighbors.csv

See also

• k-furthest-neighbor search
• k-nearest-neighbor search
• Fast approximate furthest neighbors with data-dependent candidate selection (pdf)
• Approximate furthest neighbor in high dimensions (pdf)
• QDAFN class documentation
• DrusillaSelect class documentation

mlpack_bayesian_linear_regression

BayesianLinearRegression

$ mlpack_bayesian_linear_regression [--center] [--help] [--info
        <string>] [--input_file <string>] [--input_model_file <string>]
        [--responses_file <string>] [--scale] [--test_file <string>] [--verbose]
        [--version] [--output_model_file <string>] [--predictions_file <string>]
        [--stds_file <string>]

An implementation of the bayesian linear regression. Detailed documentation.

Input options

Output options

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_file (-i) and --responses_file (-r)parameters must be given. The --center (-c)and --scale (-s) parameters control the centering and the normalizing options. A trained model can be saved with the --output_model_file (-M). If no training is desired at all, a model can be passed via the --input_model_file (-m) 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_file (-t) parameter. Predicted responses to the test points can be saved with the --predictions_file (-o) output parameter. The corresponding standard deviation can be save by precising the --stds_file (-u) parameter.

Example

For example, the following command trains a model on the data 'data.csv' and responses 'responses.csv'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.bin':

$ mlpack_bayesian_linear_regression --input_file data.csv --responses_file
  responses.csv --center --scale --output_model_file blr_model.bin

The following command uses the 'blr_model.bin' to provide predicted responses for the data 'test.csv' and save those responses to 'test_predictions.csv':

$ mlpack_bayesian_linear_regression --input_model_file blr_model.bin
  --test_file test.csv --predictions_file test_predictions.csv

Because the estimator computes a predictive distribution instead of a simple point estimate, the --stds_file (-u) parameter allows one to save the prediction uncertainties:

$ mlpack_bayesian_linear_regression --input_model_file blr_model.bin
  --test_file test.csv --predictions_file test_predictions.csv --stds_file
  stds.csv

See also

• Bayesian Interpolation
• Bayesian Linear Regression, Section 3.3
• BayesianLinearRegression C++ class documentation

mlpack_cf

Collaborative Filtering

$ mlpack_cf [--algorithm 'NMF'] [--all_user_recommendations] [--help]
        [--info <string>] [--input_model_file <string>] [--interpolation
        'average'] [--iteration_only_termination] [--max_iterations 1000]
        [--min_residue 1e-05] [--neighbor_search 'euclidean'] [--neighborhood 5]
        [--normalization 'none'] [--query_file <string>] [--rank 0]
        [--recommendations 5] [--seed 0] [--test_file <string>] [--training_file
        <string>] [--verbose] [--version] [--output_file <string>]
        [--output_model_file <string>]

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

Output options

Detailed documentation

This program performs collaborative filtering (CF) on the given dataset. Given a list of user, item and preferences (the --training_file (-t) 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_file (-m) parameter and then use that model to provide recommendations or predict values.

The input matrix should be a 3-dimensional 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_file (-q) parameter; alternately, recommendations may be generated for every user in the dataset by specifying the --all_user_recommendations (-A) parameter. In addition, the number of recommendations per user to generate can be specified with the --recommendations (-c) parameter, and the number of similar users (the size of the neighborhood) to be considered when generating recommendations can be specified with the --neighborhood (-n) parameter.

For performing the matrix decomposition, the following optimization algorithms can be specified via the --algorithm (-a) parameter:

• ‘RegSVD’ – Regularized SVD using a SGD optimizer
• ‘NMF’ – Non-negative 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 (-S) parameter:

• ‘cosine’ – Cosine Search Algorithm
• ‘euclidean’ – Euclidean Search Algorithm
• ‘pearson’ – Pearson Search Algorithm

The following weight interpolation algorithms can be specified via the --interpolation (-i) parameter:

• ‘average’ – Average Interpolation Algorithm
• ‘regression’ – Regression Interpolation Algorithm
• ‘similarity’ – Similarity Interpolation Algorithm

The following ranking normalization algorithms can be specified via the --normalization (-z) parameter:

• ‘none’ – No Normalization
• ‘item_mean’ – Item Mean Normalization
• ‘overall_mean’ – Overall Mean Normalization
• ‘user_mean’ – User Mean Normalization
• ‘z_score’ – Z-Score Normalization

A trained model may be saved to with the --output_model_file (-M) output parameter.

Example

To train a CF model on a dataset 'training_set.csv' using NMF for decomposition and saving the trained model to 'model.bin', one could call:

$ mlpack_cf --training_file training_set.csv --algorithm NMF
  --output_model_file model.bin

Then, to use this model to generate recommendations for the list of users in the query set 'users.csv', storing 5 recommendations in 'recommendations.csv', one could call

$ mlpack_cf --input_model_file model.bin --query_file users.csv
  --recommendations 5 --output_file recommendations.csv

See also

• Collaborative filtering tutorial
• Alternating Matrix Factorization tutorial
• Collaborative Filtering on Wikipedia
• Matrix factorization on Wikipedia
• Matrix factorization techniques for recommender systems (pdf)
• CFType class documentation

mlpack_dbscan

DBSCAN clustering

$ mlpack_dbscan [--epsilon 1] [--help] [--info <string>] --input_file
        <string> [--min_size 5] [--naive] [--selection_type 'ordered']
        [--single_mode] [--tree_type 'kd'] [--verbose] [--version]
        [--assignments_file <string>] [--centroids_file <string>]

An implementation of DBSCAN clustering. Given a dataset, this can compute and return a clustering of that dataset. Detailed documentation.

Input options

Output options

Detailed documentation

This program implements the DBSCAN algorithm for clustering using accelerated tree-based range search. The type of tree that is used may be parameterized, or brute-force range search may also be used.

The input dataset to be clustered may be specified with the --input_file (-i) parameter; the radius of each range search may be specified with the --epsilon (-e) parameters, and the minimum number of points in a cluster may be specified with the --min_size (-m) parameter.

The --assignments_file (-a) and --centroids_file (-C) output parameters may be used to save the output of the clustering. --assignments_file (-a) contains the cluster assignments of each point, and --centroids_file (-C) contains the centroids of each cluster.

The range search may be controlled with the --tree_type (-t), --single_mode (-S), and --naive (-N) parameters. --tree_type (-t) can control the type of tree used for range search; this can take a variety of values: ‘kd’, ‘r’, ‘r-star’, ‘x’, ‘hilbert-r’, ‘r-plus’, ‘r-plus-plus’, ‘cover’, ‘ball’. The --single_mode (-S) parameter will force single-tree search (as opposed to the default dual-tree search), and ‘--naive (-N) will force brute-force range search.

Example

An example usage to run DBSCAN on the dataset in 'input.csv' with a radius of 0.5 and a minimum cluster size of 5 is given below:

$ mlpack_dbscan --input_file input.csv --epsilon 0.5 --min_size 5

See also

• DBSCAN on Wikipedia
• A density-based algorithm for discovering clusters in large spatial databases with noise (pdf)
• DBSCAN class documentation

mlpack_decision_tree

Decision tree

$ mlpack_decision_tree [--help] [--info <string>] [--input_model_file
        <string>] [--labels_file <string>] [--maximum_depth 0]
        [--minimum_gain_split 1e-07] [--minimum_leaf_size 20]
        [--print_training_accuracy] [--print_training_error] [--test_file
        <string>] [--test_labels_file <string>] [--training_file <string>]
        [--verbose] [--version] [--weights_file <string>] [--output_model_file
        <string>] [--predictions_file <string>] [--probabilities_file <string>]

An implementation of an ID3-style 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

Output options

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_file (-t) and --labels_file (-l) parameters, respectively. The labels should be in the range [0, num_classes - 1]. Optionally, if --labels_file (-l) is not specified, the labels are assumed to be the last dimension of the training dataset.

When a model is trained, the --output_model_file (-M) output parameter may be used to save the trained model. A model may be loaded for predictions with the --input_model_file (-m) parameter. The --input_model_file (-m) parameter may not be specified when the --training_file (-t) parameter is specified. The --minimum_leaf_size (-n) parameter specifies the minimum number of training points that must fall into each leaf for it to be split. The --minimum_gain_split (-g) parameter specifies the minimum gain that is needed for the node to split. The --maximum_depth (-D) parameter specifies the maximum depth of the tree. If --print_training_error (-e) is specified, the training error will be printed.

Test data may be specified with the --test_file (-T) parameter, and if performance numbers are desired for that test set, labels may be specified with the --test_labels_file (-L) parameter. Predictions for each test point may be saved via the --predictions_file (-p) output parameter. Class probabilities for each prediction may be saved with the --probabilities_file (-P) output parameter.

Example

For example, to train a decision tree with a minimum leaf size of 20 on the dataset contained in 'data.csv' with labels 'labels.csv', saving the output model to 'tree.bin' and printing the training error, one could call

$ mlpack_decision_tree --training_file data.arff --labels_file labels.csv
  --output_model_file tree.bin --minimum_leaf_size 20 --minimum_gain_split 0.001
  --print_training_accuracy

Then, to use that model to classify points in 'test_set.csv' and print the test error given the labels 'test_labels.csv' using that model, while saving the predictions for each point to 'predictions.csv', one could call

$ mlpack_decision_tree --input_model_file tree.bin --test_file test_set.arff
  --test_labels_file test_labels.csv --predictions_file predictions.csv

See also

• Decision stump
• Random forest
• Decision trees on Wikipedia
• Induction of Decision Trees (pdf)
• DecisionTree class documentation

mlpack_det

Density Estimation With Density Estimation Trees

$ mlpack_det [--folds 10] [--help] [--info <string>] [--input_model_file
        <string>] [--max_leaf_size 10] [--min_leaf_size 5] [--path_format 'lr']
        [--skip_pruning] [--test_file <string>] [--training_file <string>]
        [--verbose] [--version] [--output_model_file <string>]
        [--tag_counters_file <string>] [--tag_file <string>]
        [--test_set_estimates_file <string>] [--training_set_estimates_file
        <string>] [--vi_file <string>]

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

Output options

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_file (-t)) using cross-validation (with number of folds specified with the --folds (-f) parameter). This trained density estimation tree may then be saved with the --output_model_file (-M) output parameter.

The variable importances (that is, the feature importance values for each dimension) may be saved with the --vi_file (-i) output parameter, and the density estimates for each training point may be saved with the --training_set_estimates_file (-e) 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 ‘lr-id’ or ‘id-lr’ are given as the --path_format (-p) 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_file (-T) 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_file (-m). The density estimates for the test points may be saved using the --test_set_estimates_file (-E) output parameter.

See also

• Density estimation tree (DET) tutorial
• Density estimation on Wikipedia
• Density estimation trees (pdf)
• DTree class documentation

mlpack_emst

Fast Euclidean Minimum Spanning Tree

$ mlpack_emst [--help] [--info <string>] --input_file <string>
        [--leaf_size 1] [--naive] [--verbose] [--version] [--output_file
        <string>]

An implementation of the Dual-Tree Boruvka algorithm for computing the Euclidean minimum spanning tree of a set of input points. Detailed documentation.

Input options

Output options

Detailed documentation

This program can compute the Euclidean minimum spanning tree of a set of input points using the dual-tree Boruvka algorithm.

The set to calculate the minimum spanning tree of is specified with the --input_file (-i) parameter, and the output may be saved with the --output_file (-o) output parameter.

The --leaf_size (-l) parameter controls the leaf size of the kd-tree that is used to calculate the minimum spanning tree, and if the --naive (-n) option is given, then brute-force 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.csv' can be calculated with a leaf size of 20 and stored as 'spanning_tree.csv' using the following command:

$ mlpack_emst --input_file data.csv --leaf_size 20 --output_file
  spanning_tree.csv

The output matrix is a three-dimensional 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

• EMST Tutorial
• Minimum spanning tree on Wikipedia
• Fast Euclidean Minimum Spanning Tree: Algorithm, Analysis, and Applications (pdf)
• DualTreeBoruvka class documentation

mlpack_fastmks

FastMKS (Fast Max-Kernel Search)

$ mlpack_fastmks [--bandwidth 1] [--base 2] [--degree 2] [--help]
        [--info <string>] [--input_model_file <string>] [--k 0] [--kernel
        'linear'] [--naive] [--offset 0] [--query_file <string>]
        [--reference_file <string>] [--scale 1] [--single] [--verbose]
        [--version] [--indices_file <string>] [--kernels_file <string>]
        [--output_model_file <string>]

An implementation of the single-tree and dual-tree fast max-kernel 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

Output options

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 (-K) parameter.

Example

For example, the following command will calculate, for each point in the query set 'query.csv', the five points in the reference set 'reference.csv' with maximum kernel evaluation using the linear kernel. The kernel evaluations may be saved with the 'kernels.csv' output parameter and the indices may be saved with the 'indices.csv' output parameter.

$ mlpack_fastmks --k 5 --reference_file reference.csv --query_file query.csv
  --indices_file indices.csv --kernels_file kernels.csv --kernel linear

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 (-b) parameter.

See also

• Fast max-kernel search tutorial (fastmks)
• k-nearest-neighbor search
• Dual-tree Fast Exact Max-Kernel Search (pdf)
• FastMKS class documentation

mlpack_gmm_train

Gaussian Mixture Model (GMM) Training

$ mlpack_gmm_train [--diagonal_covariance] --gaussians 0 [--help]
        [--info <string>] --input_file <string> [--input_model_file <string>]
        [--kmeans_max_iterations 1000] [--max_iterations 250]
        [--no_force_positive] [--noise 0] [--percentage 0.02] [--refined_start]
        [--samplings 100] [--seed 0] [--tolerance 1e-10] [--trials 1]
        [--verbose] [--version] [--output_model_file <string>]

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

Output options

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_file (-i) parameter, and the number of Gaussians in the model must be specified with the --gaussians (-g) parameter. Optionally, many trials with different random initializations may be run, and the result with highest log-likelihood on the training data will be taken. The number of trials to run is specified with the --trials (-t) 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 (-T) and --max_iterations (-n) parameters, respectively. The GMM may be initialized for training with another model, specified with the --input_model_file (-m) parameter. Otherwise, the model is initialized by running k-means on the data. The k-means clustering initialization can be controlled with the --kmeans_max_iterations (-k), --refined_start (-r), --samplings (-S), and --percentage (-p) parameters. If --refined_start (-r) is specified, then the Bradley-Fayyad 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 (-P) parameter is not specified. Alternately, adding a small amount of Gaussian noise (using the --noise (-N) parameter) to the entire dataset may help prevent Gaussians with zero variance in a particular dimension, which is usually the cause of non-invertible covariance matrices.

The --no_force_positive (-P) 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 non-positive definite covariance matrices, which will cause the program to crash.

Example

As an example, to train a 6-Gaussian GMM on the data in 'data.csv' with a maximum of 100 iterations of EM and 3 trials, saving the trained GMM to 'gmm.bin', the following command can be used:

$ mlpack_gmm_train --input_file data.csv --gaussians 6 --trials 3
  --output_model_file gmm.bin

To re-train that GMM on another set of data 'data2.csv', the following command may be used:

$ mlpack_gmm_train --input_model_file gmm.bin --input_file data2.csv
  --gaussians 6 --output_model_file new_gmm.bin

See also

• mlpack_gmm_generate
• mlpack_gmm_probability
• Gaussian Mixture Models on Wikipedia
• GMM class documentation

mlpack_gmm_generate

GMM Sample Generator

$ mlpack_gmm_generate [--help] [--info <string>] --input_model_file
        <string> --samples 0 [--seed 0] [--verbose] [--version] [--output_file
        <string>]

A sample generator for pre-trained GMMs. Given a pre-trained GMM, this can sample new points randomly from that distribution. Detailed documentation.

Input options

Output options

Detailed documentation

This program is able to generate samples from a pre-trained GMM (use gmm_train to train a GMM). The pre-trained GMM must be specified with the --input_model_file (-m) parameter. The number of samples to generate is specified by the --samples (-n) parameter. Output samples may be saved with the --output_file (-o) output parameter.

Example

The following command can be used to generate 100 samples from the pre-trained GMM 'gmm.bin' and store those generated samples in 'samples.csv':

$ mlpack_gmm_generate --input_model_file gmm.bin --samples 100 --output_file
  samples.csv

See also

• mlpack_gmm_train
• mlpack_gmm_probability
• Gaussian Mixture Models on Wikipedia
• GMM class documentation

mlpack_gmm_probability

GMM Probability Calculator

$ mlpack_gmm_probability [--help] [--info <string>] --input_file
        <string> --input_model_file <string> [--verbose] [--version]
        [--output_file <string>]

A probability calculator for GMMs. Given a pre-trained GMM and a set of points, this can compute the probability that each point is from the given GMM. Detailed documentation.

Input options

Output options

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_file (-m) parameter, and the points are specified with the --input_file (-i) parameter. The output probabilities may be saved via the --output_file (-o) output parameter.

Example

So, for example, to calculate the probabilities of each point in 'points.csv' coming from the pre-trained GMM 'gmm.bin', while storing those probabilities in 'probs.csv', the following command could be used:

$ mlpack_gmm_probability --input_model_file gmm.bin --input_file points.csv
  --output_file probs.csv

See also

• mlpack_gmm_train
• mlpack_gmm_generate
• Gaussian Mixture Models on Wikipedia
• GMM class documentation

mlpack_hmm_train

Hidden Markov Model (HMM) Training

$ mlpack_hmm_train [--batch] [--gaussians 0] [--help] [--info <string>]
        --input_file <string> [--input_model_file <string>] [--labels_file
        <string>] [--seed 0] [--states 0] [--tolerance 1e-05] [--type
        'gaussian'] [--verbose] [--version] [--output_model_file <string>]

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

Output options

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 (-i)), or, a file containing files in which input sequences can be found (when --input_file (-i)and--batch (-b) are used together). In addition, labels can be provided in the file specified by --labels_file (-l), and if --batch (-b) is used, the file given to --labels_file (-l) should contain a list of files of labels corresponding to the sequences in the file given to --input_file (-i).

The HMM is trained with the Baum-Welch algorithm if no labels are provided. The tolerance of the Baum-Welch algorithm can be set with the --tolerance (-T)option. By default, the transition matrix is randomly initialized and the emission distributions are initialized to fit the extent of the data.

Optionally, a pre-created HMM model can be used as a guess for the transition matrix and emission probabilities; this is specifiable with --output_model_file (-M).

See also

• mlpack_hmm_generate
• mlpack_hmm_loglik
• mlpack_hmm_viterbi
• Hidden Mixture Models on Wikipedia
• HMM class documentation

mlpack_hmm_generate

Hidden Markov Model (HMM) Sequence Generator

$ mlpack_hmm_generate [--help] [--info <string>] --length 0 --model_file
        <string> [--seed 0] [--start_state 0] [--verbose] [--version]
        [--output_file <string>] [--state_file <string>]

A utility to generate random sequences from a pre-trained 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

Output options

Detailed documentation

This utility takes an already-trained HMM, specified as the --model_file (-m) parameter, and generates a random observation sequence and hidden state sequence based on its parameters. The observation sequence may be saved with the --output_file (-o) output parameter, and the internal state sequence may be saved with the --state_file (-S) output parameter.

The state to start the sequence in may be specified with the --start_state (-t) parameter.

Example

For example, to generate a sequence of length 150 from the HMM 'hmm.bin' and save the observation sequence to 'observations.csv' and the hidden state sequence to 'states.csv', the following command may be used:

$ mlpack_hmm_generate --model_file hmm.bin --length 150 --output_file
  observations.csv --state_file states.csv

See also

• mlpack_hmm_train
• mlpack_hmm_loglik
• mlpack_hmm_viterbi
• Hidden Mixture Models on Wikipedia
• HMM class documentation

mlpack_hmm_loglik

Hidden Markov Model (HMM) Sequence Log-Likelihood

$ mlpack_hmm_loglik [--help] [--info <string>] --input_file <string>
        --input_model_file <string> [--verbose] [--version] [--log_likelihood
        0]

A utility for computing the log-likelihood of a sequence for Hidden Markov Models (HMMs). Given a pre-trained HMM and an observation sequence, this computes and returns the log-likelihood of that sequence being observed from that HMM. Detailed documentation.

Input options

Output options

Detailed documentation

This utility takes an already-trained HMM, specified with the --input_model_file (-m) parameter, and evaluates the log-likelihood of a sequence of observations, given with the --input_file (-i) parameter. The computed log-likelihood is given as output.

Example

For example, to compute the log-likelihood of the sequence 'seq.csv' with the pre-trained HMM 'hmm.bin', the following command may be used:

$ mlpack_hmm_loglik --input_file seq.csv --input_model_file hmm.bin

See also

• mlpack_hmm_train
• mlpack_hmm_generate
• mlpack_hmm_viterbi
• Hidden Mixture Models on Wikipedia
• HMM class documentation

mlpack_hmm_viterbi

Hidden Markov Model (HMM) Viterbi State Prediction

$ mlpack_hmm_viterbi [--help] [--info <string>] --input_file <string>
        --input_model_file <string> [--verbose] [--version] [--output_file
        <string>]

A utility for computing the most probable hidden state sequence for Hidden Markov Models (HMMs). Given a pre-trained HMM and an observed sequence, this uses the Viterbi algorithm to compute and return the most probable hidden state sequence. Detailed documentation.

Input options

Output options

Detailed documentation

This utility takes an already-trained HMM, specified as --input_model_file (-m), and evaluates the most probable hidden state sequence of a given sequence of observations (specified as ‘--input_file (-i), using the Viterbi algorithm. The computed state sequence may be saved using the --output_file (-o) output parameter.

Example

For example, to predict the state sequence of the observations 'obs.csv' using the HMM 'hmm.bin', storing the predicted state sequence to 'states.csv', the following command could be used:

$ mlpack_hmm_viterbi --input_file obs.csv --input_model_file hmm.bin
  --output_file states.csv

See also

• mlpack_hmm_train
• mlpack_hmm_generate
• mlpack_hmm_loglik
• Hidden Mixture Models on Wikipedia
• HMM class documentation

mlpack_hoeffding_tree

Hoeffding trees

$ mlpack_hoeffding_tree [--batch_mode] [--bins 10] [--confidence 0.95]
        [--help] [--info <string>] [--info_gain] [--input_model_file <string>]
        [--labels_file <string>] [--max_samples 5000] [--min_samples 100]
        [--numeric_split_strategy 'binary'] [--observations_before_binning 100]
        [--passes 1] [--test_file <string>] [--test_labels_file <string>]
        [--training_file <string>] [--verbose] [--version] [--output_model_file
        <string>] [--predictions_file <string>] [--probabilities_file <string>]

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 pre-trained Hoeffding tree can be used for predicting the classifications of new points. Detailed documentation.

Input options

Output options

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_file (-t) and --labels_file (-l) parameters, respectively. Optionally, if --labels_file (-l) 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 (-b) 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_file (-M) output parameter. A model may be loaded from file for further training or testing with the --input_model_file (-m) parameter.

Test data may be specified with the --test_file (-T) parameter, and if performance statistics are desired for that test set, labels may be specified with the --test_labels_file (-L) parameter. Predictions for each test point may be saved with the --predictions_file (-p) output parameter, and class probabilities for each prediction may be saved with the --probabilities_file (-P) output parameter.

Example

For example, to train a Hoeffding tree with confidence 0.99 with data 'dataset.csv', saving the trained tree to 'tree.bin', the following command may be used:

$ mlpack_hoeffding_tree --training_file dataset.arff --confidence 0.99
  --output_model_file tree.bin

Then, this tree may be used to make predictions on the test set 'test_set.csv', saving the predictions into 'predictions.csv' and the class probabilities into 'class_probs.csv' with the following command:

$ mlpack_hoeffding_tree --input_model_file tree.bin --test_file test_set.arff
  --predictions_file predictions.csv --probabilities_file class_probs.csv

See also

• mlpack_decision_tree
• mlpack_random_forest
• Mining High-Speed Data Streams (pdf)
• HoeffdingTree class documentation

mlpack_kde

Kernel Density Estimation

$ mlpack_kde [--abs_error 0] [--algorithm 'dual-tree'] [--bandwidth 1]
        [--help] [--info <string>] [--initial_sample_size 100]
        [--input_model_file <string>] [--kernel 'gaussian'] [--mc_break_coef
        0.4] [--mc_entry_coef 3] [--mc_probability 0.95] [--monte_carlo]
        [--query_file <string>] [--reference_file <string>] [--rel_error 0.05]
        [--tree 'kd-tree'] [--verbose] [--version] [--output_model_file
        <string>] [--predictions_file <string>]

An implementation of kernel density estimation with dual-tree 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

Output options

Detailed documentation

This program performs a Kernel Density Estimation. KDE is a non-parametric 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 (-e) as well as the maximum absolute error tolerance with the parameter --abs_error (-E). This program runs using an Euclidean metric. Kernel function can be selected using the --kernel (-k) option. You can also choose what which type of tree to use for the dual-tree algorithm with --tree (-t). It is also possible to select whether to use dual-tree algorithm or single-tree algorithm using the --algorithm (-a) 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 (-S) flag can be used, and success probability can be set with the --mc_probability (-P) option. It is possible to set the initial sample size for the Monte Carlo estimation using --initial_sample_size (-s). 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 (-C). 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 (-c).

Example

For example, the following will run KDE using the data in 'ref_data.csv' for training and the data in 'qu_data.csv' as query data. It will apply an Epanechnikov kernel with a 0.2 bandwidth to each reference point and use a KD-Tree for the dual-tree optimization. The returned predictions will be within 5% of the real KDE value for each query point.

$ mlpack_kde --reference_file ref_data.csv --query_file qu_data.csv
  --bandwidth 0.2 --kernel epanechnikov --tree kd-tree --rel_error 0.05
  --predictions_file out_data.csv

the predicted density estimations will be stored in 'out_data.csv'. If no --query_file (-q) is provided, then KDE will be computed on the --reference_file (-r) 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 (-b)) 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.

$ mlpack_kde --reference_file ref_data.csv --query_file qu_data.csv
  --bandwidth 0.2 --kernel gaussian --tree kd-tree --rel_error 0.05
  --predictions_file out_data.csv --monte_carlo --mc_probability 0.95
  --initial_sample_size 200 --mc_entry_coef 3.5 --mc_break_coef 0.6

See also

• mlpack_knn
• Kernel density estimation on Wikipedia
• Tree-Independent Dual-Tree Algorithms
• Fast High-dimensional Kernel Summations Using the Monte Carlo Multipole Method
• KDE C++ class documentation

mlpack_kernel_pca

Kernel Principal Components Analysis

$ mlpack_kernel_pca [--bandwidth 1] [--center] [--degree 1] [--help]
        [--info <string>] --input_file <string> --kernel <string>
        [--kernel_scale 1] [--new_dimensionality 0] [--nystroem_method]
        [--offset 0] [--sampling 'kmeans'] [--verbose] [--version]
        [--output_file <string>]

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

Output options

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 (-b), --kernel_scale (-S), --offset (-O), or --degree (-D) (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 (-n) 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 (-s) 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.csv' using the Gaussian kernel, and saving the transformed data to 'transformed.csv':

$ mlpack_kernel_pca --input_file input.csv --kernel gaussian --output_file
  transformed.csv

See also

• Kernel principal component analysis on Wikipedia
• Kernel Principal Component Analysis (pdf)
• KernelPCA class documentation

mlpack_kmeans

K-Means Clustering

$ mlpack_kmeans [--algorithm 'naive'] [--allow_empty_clusters]
        --clusters 0 [--help] [--in_place] [--info <string>]
        [--initial_centroids_file <string>] --input_file <string>
        [--kill_empty_clusters] [--kmeans_plus_plus] [--labels_only]
        [--max_iterations 1000] [--percentage 0.02] [--refined_start]
        [--samplings 100] [--seed 0] [--verbose] [--version] [--centroid_file
        <string>] [--output_file <string>]

An implementation of several strategies for efficient k-means clustering. Given a dataset and a value of k, this computes and returns a k-means clustering on that data. Detailed documentation.

Input options

Output options

Detailed documentation

This program performs K-Means 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 k-means++ algorithm can be used to choose initial centroids with the --kmeans_plus_plus (-K) parameter. The Bradley and Fayyad approach (“Refining initial points for k-means clustering”, 1998) can be used to select initial points by specifying the --refined_start (-r) parameter. This approach works by taking random samplings of the dataset; to specify the number of samplings, the --samplings (-S) parameter is used, and to specify the percentage of the dataset to be used in each sample, the --percentage (-p) 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 (-a) option. The standard O(kN) approach can be used (‘naive’). Other options include the Pelleg-Moore tree-based algorithm (‘pelleg-moore’), Elkan’s triangle-inequality based algorithm (‘elkan’), Hamerly’s modification to Elkan’s algorithm (‘hamerly’), the dual-tree k-means algorithm (‘dualtree’), and the dual-tree k-means algorithm using the cover tree (‘dualtree-covertree’).

The behavior for when an empty cluster is encountered can be modified with the --allow_empty_clusters (-e) 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 (-E) 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 time-consuming to calculate; therefore, specifying either of these parameters will often accelerate runtime.

Initial clustering assignments may be specified using the --initial_centroids_file (-I) parameter, and the maximum number of iterations may be specified with the --max_iterations (-m) parameter.

Example

As an example, to use Hamerly’s algorithm to perform k-means clustering with k=10 on the dataset 'data.csv', saving the centroids to 'centroids.csv' and the assignments for each point to 'assignments.csv', the following command could be used:

$ mlpack_kmeans --input_file data.csv --clusters 10 --output_file
  assignments.csv --centroid_file centroids.csv

To run k-means on that same dataset with initial centroids specified in 'initial.csv' with a maximum of 500 iterations, storing the output centroids in 'final.csv' the following command may be used:

$ mlpack_kmeans --input_file data.csv --initial_centroids_file initial.csv
  --clusters 10 --max_iterations 500 --centroid_file final.csv

See also

• K-Means tutorial
• mlpack_dbscan
• k-means++
• Using the triangle inequality to accelerate k-means (pdf)
• Making k-means even faster (pdf)
• Accelerating exact k-means algorithms with geometric reasoning (pdf)
• A dual-tree algorithm for fast k-means clustering with large k (pdf)
• KMeans class documentation

mlpack_lars

LARS

$ mlpack_lars [--help] [--info <string>] [--input_file <string>]
        [--input_model_file <string>] [--lambda1 0] [--lambda2 0]
        [--responses_file <string>] [--test_file <string>] [--use_cholesky]
        [--verbose] [--version] [--output_model_file <string>]
        [--output_predictions_file <string>]

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 pre-trained model to output regression predictions for a test set. Detailed documentation.

Input options

Output options

Detailed documentation

An implementation of LARS: Least Angle Regression (Stagewise/laSso). This is a stage-wise homotopy-based algorithm for L1-regularized linear regression (LASSO) and L1+L2-regularized 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 (-l) = 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_file (-i) and --responses_file (-r) parameters must be given. The --lambda1 (-l), --lambda2 (-L), and --use_cholesky (-c) parameters control the training options. A trained model can be saved with the --output_model_file (-M). If no training is desired at all, a model can be passed via the --input_model_file (-m) 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_file (-t) parameter. Predicted responses to the test points can be saved with the --output_predictions_file (-o) output parameter.

Example

For example, the following command trains a model on the data 'data.csv' and responses 'responses.csv' 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.bin':

$ mlpack_lars --input_file data.csv --responses_file responses.csv --lambda1
  0.4 --lambda2 0 --output_model_file lasso_model.bin

The following command uses the 'lasso_model.bin' to provide predicted responses for the data 'test.csv' and save those responses to 'test_predictions.csv':

$ mlpack_lars --input_model_file lasso_model.bin --test_file test.csv
  --output_predictions_file test_predictions.csv

See also

• mlpack_linear_regression
• Least angle regression (pdf)
• LARS C++ class documentation

mlpack_linear_svm

Linear SVM is an L2-regularized support vector machine.

$ mlpack_linear_svm [--delta 1] [--epochs 50] [--help] [--info <string>]
        [--input_model_file <string>] [--labels_file <string>] [--lambda 0.0001]
        [--max_iterations 10000] [--no_intercept] [--num_classes 0] [--optimizer
        'lbfgs'] [--seed 0] [--shuffle] [--step_size 0.01] [--test_file
        <string>] [--test_labels_file <string>] [--tolerance 1e-10]
        [--training_file <string>] [--verbose] [--version] [--output_model_file
        <string>] [--predictions_file <string>] [--probabilities_file <string>]

An implementation of linear SVM for multiclass classification. Given labeled data, a model can be trained and saved for future use; or, a pre-trained model can be used to classify new points. Detailed documentation.

Input options

Output options

Detailed documentation

An implementation of linear SVMs that uses either L-BFGS or parallel SGD (stochastic gradient descent) to train the model.

This program allows loading a linear SVM model (via the --input_model_file (-m) parameter) or training a linear SVM model given training data (specified with the --training_file (-t) parameter), or both those things at once. In addition, this program allows classification on a test dataset (specified with the --test_file (-T) parameter) and the classification results may be saved with the --predictions_file (-P) output parameter. The trained linear SVM model may be saved using the --output_model_file (-M) output parameter.

The training data, if specified, may have class labels as its last dimension. Alternately, the --labels_file (-l) 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 (-r) option, and the number of classes can be manually specified with the --num_classes (-c)and if an intercept term is not desired in the model, the --no_intercept (-N) parameter can be specified.Margin of difference between correct class and other classes can be specified with the --delta (-d) option.The optimizer used to train the model can be specified with the --optimizer (-O) parameter. Available options are ‘psgd’ (parallel stochastic gradient descent) and ‘lbfgs’ (the L-BFGS optimizer). There are also various parameters for the optimizer; the --max_iterations (-n) parameter specifies the maximum number of allowed iterations, and the --tolerance (-e) parameter specifies the tolerance for convergence. For the parallel SGD optimizer, the --step_size (-a) parameter controls the step size taken at each iteration by the optimizer and the maximum number of epochs (specified with --epochs (-E)). 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_file (-T) is specified. The --test_file (-T) parameter can be specified without the --training_file (-t) parameter, so long as an existing linear SVM model is given with the --input_model_file (-m) parameter. The output predictions from the linear SVM model may be saved with the --predictions_file (-P) parameter.

Example

As an example, to train a LinaerSVM on the data ‘'data.csv'’ with labels ‘'labels.csv'’ with L2 regularization of 0.1, saving the model to ‘'lsvm_model.bin'’, the following command may be used:

$ mlpack_linear_svm --training_file data.csv --labels_file labels.csv --lambda
  0.1 --delta 1 --num_classes 0 --output_model_file lsvm_model.bin

Then, to use that model to predict classes for the dataset ‘'test.csv'’, storing the output predictions in ‘'predictions.csv'’, the following command may be used:

$ mlpack_linear_svm --input_model_file lsvm_model.bin --test_file test.csv
  --predictions_file predictions.csv

See also

• mlpack_random_forest
• mlpack_logistic_regression
• LinearSVM on Wikipedia
• LinearSVM C++ class documentation

mlpack_lmnn

Large Margin Nearest Neighbors (LMNN)

$ mlpack_lmnn [--batch_size 50] [--center] [--distance_file <string>]
        [--help] [--info <string>] --input_file <string> [--k 1] [--labels_file
        <string>] [--linear_scan] [--max_iterations 100000] [--normalize]
        [--optimizer 'amsgrad'] [--passes 50] [--print_accuracy] [--range 1]
        [--rank 0] [--regularization 0.5] [--seed 0] [--step_size 0.01]
        [--tolerance 1e-07] [--verbose] [--version] [--centered_data_file
        <string>] [--output_file <string>] [--transformed_data_file <string>]

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 k-nearest-neighbor performance; this can be useful as a preprocessing step. Detailed documentation.

Input options

Output options

Detailed documentation

This program implements Large Margin Nearest Neighbors, a distance learning technique. The method seeks to improve k-nearest-neighbor 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_file (-i)), or alternatively as a separate matrix (specified with --labels_file (-l)). Additionally, a starting point for optimization (specified with --distance_file (-d)can be given, having (r x d) dimensionality. Here r should satisfy 1 <= r <= d, Consequently a Low-Rank matrix will be optimized. Alternatively, Low-Rank distance can be learned by specifying the --rank (-A)parameter (A Low-Rank 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 (-k)), A regularization parameter can also be passed, It acts as a trade of between the pulling and pushing terms (specified with --regularization (-r)), In addition, this implementation of LMNN includes a parameter to decide the interval after which impostors must be re-calculated (specified with --range (-R)).

Output can either be the learned distance matrix (specified with --output_file (-o)), or the transformed dataset (specified with --transformed_data_file (-D)), or both. Additionally mean-centered dataset (specified with --centered_data_file (-c)) can be accessed given mean-centering (specified with --center (-C)) is performed on the dataset. Accuracy on initial dataset and final transformed dataset can be printed by specifying the --print_accuracy (-P)parameter.

This implementation of LMNN uses AdaGrad, BigBatch_SGD, stochastic gradient descent, mini-batch stochastic gradient descent, or the L_BFGS optimizer.

AdaGrad, specified by the value ‘adagrad’ for the parameter --optimizer (-O), uses maximum of past squared gradients. It primarily on six parameters: the step size (specified with --step_size (-a)), the batch size (specified with --batch_size (-b)), the maximum number of passes (specified with --passes (-p)). Inaddition, a normalized starting point can be used by specifying the --normalize (-N) parameter.

BigBatch_SGD, specified by the value ‘bbsgd’ for the parameter --optimizer (-O), depends primarily on four parameters: the step size (specified with --step_size (-a)), the batch size (specified with --batch_size (-b)), the maximum number of passes (specified with --passes (-p)). In addition, a normalized starting point can be used by specifying the --normalize (-N) parameter.

Stochastic gradient descent, specified by the value ‘sgd’ for the parameter --optimizer (-O), depends primarily on three parameters: the step size (specified with --step_size (-a)), the batch size (specified with --batch_size (-b)), and the maximum number of passes (specified with --passes (-p)). In addition, a normalized starting point can be used by specifying the --normalize (-N) parameter. Furthermore, mean-centering can be performed on the dataset by specifying the --center (-C)parameter.

The L-BFGS optimizer, specified by the value ‘lbfgs’ for the parameter --optimizer (-O), uses a back-tracking line search algorithm to minimize a function. The following parameters are used by L-BFGS: --max_iterations (-n), --tolerance (-t)(the optimization is terminated when the gradient norm is below this value). For more details on the L-BFGS optimizer, consult either the mlpack L-BFGS documentation (in lbfgs.hpp) or the vast set of published literature on L-BFGS. In addition, a normalized starting point can be used by specifying the --normalize (-N) 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:

$ mlpack_lmnn --input_file iris.csv --labels_file iris_labels.csv --k 3
  --optimizer bbsgd --output_file output.csv

An another program call making use of range & regularization parameter with dataset having labels as last column can be made as:

$ mlpack_lmnn --input_file letter_recognition.csv --k 5 --range 10
  --regularization 0.4 --output_file output.csv

See also

• mlpack_nca
• Large margin nearest neighbor on Wikipedia
• Distance metric learning for large margin nearest neighbor classification (pdf)
• LMNN C++ class documentation

mlpack_local_coordinate_coding

Local Coordinate Coding

$ mlpack_local_coordinate_coding [--atoms 0] [--help] [--info <string>]
        [--initial_dictionary_file <string>] [--input_model_file <string>]
        [--lambda 0] [--max_iterations 0] [--normalize] [--seed 0] [--test_file
        <string>] [--tolerance 0.01] [--training_file <string>] [--verbose]
        [--version] [--codes_file <string>] [--dictionary_file <string>]
        [--output_model_file <string>]

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

Output options

Detailed documentation

An implementation of Local Coordinate Coding (LCC), which codes data that approximately lives on a manifold using a variation of l1-norm 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_file (-i) parameter. The l1-norm regularization parameter is specified with the --lambda (-l) parameter.

Example

For example, to run LCC on the dataset 'data.csv' using 200 atoms and an l1-regularization parameter of 0.1, saving the dictionary --dictionary_file (-d) and the codes into --codes_file (-c), use

$ mlpack_local_coordinate_coding --training_file data.csv --atoms 200 --lambda
  0.1 --dictionary_file dict.csv --codes_file codes.csv

The maximum number of iterations may be specified with the --max_iterations (-n) parameter. Optionally, the input data matrix X can be normalized before coding with the --normalize (-N) parameter.

An LCC model may be saved using the --output_model_file (-M) output parameter. Then, to encode new points from the dataset 'points.csv' with the previously saved model 'lcc_model.bin', saving the new codes to 'new_codes.csv', the following command can be used:

$ mlpack_local_coordinate_coding --input_model_file lcc_model.bin --test_file
  points.csv --codes_file new_codes.csv

See also

• mlpack_sparse_coding
• Nonlinear learning using local coordinate coding (pdf)
• LocalCoordinateCoding C++ class documentation

mlpack_logistic_regression

L2-regularized Logistic Regression and Prediction

$ mlpack_logistic_regression [--batch_size 64] [--decision_boundary 0.5]
        [--help] [--info <string>] [--input_model_file <string>] [--labels_file
        <string>] [--lambda 0] [--max_iterations 10000] [--optimizer 'lbfgs']
        [--step_size 0.01] [--test_file <string>] [--tolerance 1e-10]
        [--training_file <string>] [--verbose] [--version] [--output_model_file
        <string>] [--predictions_file <string>] [--probabilities_file <string>]

An implementation of L2-regularized logistic regression for two-class classification. Given labeled data, a model can be trained and saved for future use; or, a pre-trained model can be used to classify new points. Detailed documentation.

Input options

Output options

Detailed documentation

An implementation of L2-regularized logistic regression using either the L-BFGS 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_file (-m) parameter) or training a logistic regression model given training data (specified with the --training_file (-t) parameter), or both those things at once. In addition, this program allows classification on a test dataset (specified with the --test_file (-T) parameter) and the classification results may be saved with the --predictions_file (-P) output parameter. The trained logistic regression model may be saved using the --output_model_file (-M) output parameter.

The training data, if specified, may have class labels as its last dimension. Alternately, the --labels_file (-l) 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 (-L) option, and the optimizer used to train the model can be specified with the --optimizer (-O) parameter. Available options are ‘sgd’ (stochastic gradient descent) and ‘lbfgs’ (the L-BFGS optimizer). There are also various parameters for the optimizer; the --max_iterations (-n) parameter specifies the maximum number of allowed iterations, and the --tolerance (-e) parameter specifies the tolerance for convergence. For the SGD optimizer, the --step_size (-s) parameter controls the step size taken at each iteration by the optimizer. The batch size for SGD is controlled with the --batch_size (-b) 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 (-n) 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_file (-T) is specified. The --test_file (-T) parameter can be specified without the --training_file (-t) parameter, so long as an existing logistic regression model is given with the --input_model_file (-m) parameter. The output predictions from the logistic regression model may be saved with the --predictions_file (-P) parameter.

This implementation of logistic regression does not support the general multi-class case but instead only the two-class 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.csv'’ with labels ‘'labels.csv'’ with L2 regularization of 0.1, saving the model to ‘'lr_model.bin'’, the following command may be used:

$ mlpack_logistic_regression --training_file data.csv --labels_file labels.csv
  --lambda 0.1 --output_model_file lr_model.bin

Then, to use that model to predict classes for the dataset ‘'test.csv'’, storing the output predictions in ‘'predictions.csv'’, the following command may be used:

$ mlpack_logistic_regression --input_model_file lr_model.bin --test_file
  test.csv --predictions_file predictions.csv

See also

• mlpack_softmax_regression
• mlpack_random_forest
• Logistic regression on Wikipedia
• :LogisticRegression C++ class documentation

mlpack_lsh

K-Approximate-Nearest-Neighbor Search with LSH

$ mlpack_lsh [--bucket_size 500] [--hash_width 0] [--help] [--info
        <string>] [--input_model_file <string>] [--k 0] [--num_probes 0]
        [--projections 10] [--query_file <string>] [--reference_file <string>]
        [--second_hash_size 99901] [--seed 0] [--tables 30]
        [--true_neighbors_file <string>] [--verbose] [--version]
        [--distances_file <string>] [--neighbors_file <string>]
        [--output_model_file <string>]

An implementation of approximate k-nearest-neighbor search with locality-sensitive 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

Output options

Detailed documentation

This program will calculate the k approximate-nearest-neighbors of a set of points using locality-sensitive 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.csv' and store the distances in 'distances.csv' and the neighbors in 'neighbors.csv':

$ mlpack_lsh --k 5 --reference_file input.csv --distances_file distances.csv
  --neighbors_file neighbors.csv

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 approximate-nearest-neighbors search, results may be different from run to run. Thus, the --seed (-s) parameter can be specified to set the random seed.

This program also has many other parameters to control its functionality; see the parameter-specific documentation for more information.

See also

• mlpack_knn
• mlpack_krann
• Locality-sensitive hashing on Wikipedia
• Locality-sensitive hashing scheme based on p-stable distributions(pdf)
• LSHSearch C++ class documentation

mlpack_mean_shift

Mean Shift Clustering

$ mlpack_mean_shift [--force_convergence] [--help] [--in_place] [--info
        <string>] --input_file <string> [--labels_only] [--max_iterations 1000]
        [--radius 0] [--verbose] [--version] [--centroid_file <string>]
        [--output_file <string>]

A fast implementation of mean-shift clustering using dual-tree range search. Given a dataset, this uses the mean shift algorithm to produce and return a clustering of the data. Detailed documentation.

Input options

Output options

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_file (-i) parameter, and the radius used for search can be specified with the --radius (-r) parameter. The maximum number of iterations before algorithm termination is controlled with the --max_iterations (-m) parameter.

The output labels may be saved with the --output_file (-o) output parameter and the centroids of each cluster may be saved with the --centroid_file (-C) output parameter.

Example

For example, to run mean shift clustering on the dataset 'data.csv' and store the centroids to 'centroids.csv', the following command may be used:

$ mlpack_mean_shift --input_file data.csv --centroid_file centroids.csv

See also

• mlpack_kmeans
• mlpack_dbscan
• Mean shift on Wikipedia
• Mean Shift, Mode Seeking, and Clustering (pdf)
• mlpack::mean_shift::MeanShift C++ class documentation

mlpack_nbc

Parametric Naive Bayes Classifier

$ mlpack_nbc [--help] [--incremental_variance] [--info <string>]
        [--input_model_file <string>] [--labels_file <string>] [--test_file
        <string>] [--training_file <string>] [--verbose] [--version]
        [--output_file <string>] [--output_model_file <string>]
        [--output_probs_file <string>] [--predictions_file <string>]
        [--probabilities_file <string>]

An implementation of the Naive Bayes Classifier, used for classification. Given labeled data, an NBC model can be trained and saved, or, a pre-trained model can be used for classification. Detailed documentation.

Input options

Output options

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_file (-t) parameter. Labels may be either the last row of the training set, or alternately the --labels_file (-l) parameter may be specified to pass a separate matrix of labels.

If training is not desired, a pre-existing model may be loaded with the --input_model_file (-m) parameter.

The --incremental_variance (-I) 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_file (-T) parameter, and the classifications may be saved with the --predictions_file (-a)predictions parameter. If saving the trained model is desired, this may be done with the --output_model_file (-M) output parameter.

Note: the --output_file (-o) and --output_probs_file parameters are deprecated and will be removed in mlpack 4.0.0. Use --predictions_file (-a) and --probabilities_file (-p) instead.

Example

For example, to train a Naive Bayes classifier on the dataset 'data.csv' with labels 'labels.csv' and save the model to 'nbc_model.bin', the following command may be used:

$ mlpack_nbc --training_file data.csv --labels_file labels.csv
  --output_model_file nbc_model.bin

Then, to use 'nbc_model.bin' to predict the classes of the dataset 'test_set.csv' and save the predicted classes to 'predictions.csv', the following command may be used:

$ mlpack_nbc --input_model_file nbc_model.bin --test_file test_set.csv
  --output_file predictions.csv

See also

• mlpack_softmax_regression
• mlpack_random_forest
• Naive Bayes classifier on Wikipedia
• NaiveBayesClassifier C++ class documentation

mlpack_nca

Neighborhood Components Analysis (NCA)

$ mlpack_nca [--armijo_constant 0.0001] [--batch_size 50] [--help]
        [--info <string>] --input_file <string> [--labels_file <string>]
        [--linear_scan] [--max_iterations 500000] [--max_line_search_trials 50]
        [--max_step 1e+20] [--min_step 1e-20] [--normalize] [--num_basis 5]
        [--optimizer 'sgd'] [--seed 0] [--step_size 0.01] [--tolerance 1e-07]
        [--verbose] [--version] [--wolfe 0.9] [--output_file <string>]

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 k-nearest-neighbor classification, and returns the learned distance metric. Detailed documentation.

Input options

Output options

Detailed documentation

This program implements Neighborhood Components Analysis, both a linear dimensionality reduction technique and a distance learning technique. The method seeks to improve k-nearest-neighbor 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_file (-i)), or alternatively as a separate matrix (specified with --labels_file (-l)).

This implementation of NCA uses stochastic gradient descent, mini-batch 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 (-O), depends primarily on three parameters: the step size (specified with --step_size (-a)), the batch size (specified with --batch_size (-b)), and the maximum number of iterations (specified with --max_iterations (-n)). In addition, a normalized starting point can be used by specifying the --normalize (-N) 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 zero-valued 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 (-t)) 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 (-n) parameter equal to the number of points in the dataset.

The L-BFGS optimizer, specified by the value ‘lbfgs’ for the parameter --optimizer (-O), uses a back-tracking line search algorithm to minimize a function. The following parameters are used by L-BFGS: --num_basis (-B) (specifies the number of memory points used by L-BFGS), --max_iterations (-n), --armijo_constant (-A), --wolfe (-w), --tolerance (-t) (the optimization is terminated when the gradient norm is below this value), --max_line_search_trials (-T), --min_step (-m), and --max_step (-M) (which both refer to the line search routine). For more details on the L-BFGS optimizer, consult either the mlpack L-BFGS documentation (in lbfgs.hpp) or the vast set of published literature on L-BFGS.

By default, the SGD optimizer is used.

See also

• mlpack_lmnn
• Neighbourhood components analysis on Wikipedia
• Neighbourhood components analysis (pdf)
• NCA C++ class documentation