🔗 LinearSVM

The LinearSVM class implements an L2-regularized support vector machine for numerical data that can train using any ensmallen optimizer. The class offers standard classification functionality. Linear SVM is useful for multi-class classification (i.e. classes are 0, 1, 2, etc.).

Simple usage example:

// Train a linear SVM classifier on random data and predict labels:

// All data and labels are uniform random; 5 dimensional data, 4 classes.
// Replace with a data::Load() call or similar for a real application.
arma::mat dataset(5, 1000, arma::fill::randu); // 1000 points.
arma::Row<size_t> labels =
    arma::randi<arma::Row<size_t>>(1000, arma::distr_param(0, 3));
arma::mat testDataset(5, 500, arma::fill::randu); // 500 test points.

mlpack::LinearSVM svm;                  // Step 1: create model.
svm.Train(dataset, labels, 4);          // Step 2: train model.
arma::Row<size_t> predictions;
svm.Classify(testDataset, predictions); // Step 3: classify points.

// Print some information about the test predictions.
std::cout << arma::accu(predictions == 1) << " test points classified as class "
    << "1." << std::endl;

More examples...

See also:

🔗 Constructors

Constructor Parameters:

name type description default
data arma::mat Column-major training matrix. (N/A)
labels arma::Row<size_t> Training labels, between 0 and numClasses - 1 (inclusive). Should have length data.n_cols. (N/A)
dimensionality size_t Dimension of input data (if data is not specified). Should be equal to data.n_rows. (N/A)
numClasses size_t Number of classes in the dataset. (N/A)
optimizer any ensmallen optimizer Instantiated ensmallen optimizer for differentiable functions or differentiable separable functions. ens::L_BFGS()
lambda double L2 regularization penalty parameter. Must be nonnegative. 0.0
delta double Margin of difference between correct class and other classes. 1.0
fitIntercept bool If true, then an intercept term is fitted to the model. false
callbacks... any set of ensmallen callbacks Optional callbacks for the ensmallen optimizer, such as e.g. ens::ProgressBar(), ens::Report(), or others. (N/A)

As an alternative to passing lambda, delta, or fitIntercept, these can be set with a standalone method. The following functions can be used before calling Train():

🔗 Training

If training is not done as part of the constructor call, it can be done with the Train() function:

Types of each argument are the same as in the table for constructors above.

Note: Training is not incremental. Successive calls to Train() will train entirely new models.

🔗 Classification

Once a LinearSVM model is trained, the Classify() member function can be used to make class predictions for new data.

Classification Parameters:

usage name type description
single-point point arma::vec Single point for classification.
single-point prediction size_t& size_t to store class prediction into.
single-point probabilitiesVec arma::vec& arma::vec& to store class probabilities into; will have length 2.
multi-point data arma::mat Set of column-major points for classification.
multi-point predictions arma::Row<size_t>& Vector of size_ts to store class prediction into; will be set to length data.n_cols.
multi-point probabilities arma::mat& Matrix to store class probabilities into (number of rows will be equal to 2; number of columns will be equal to data.n_cols).

🔗 Other Functionality

🔗 Simple Examples

See also the simple usage example for a trivial usage of the LinearSVM class.

Train a linear SVM using a custom SGD-like optimizer with callbacks.

// See
arma::mat dataset;
mlpack::data::Load("satellite.train.csv", dataset, true);
// See
arma::Row<size_t> labels;
mlpack::data::Load("satellite.train.labels.csv", labels, true);

mlpack::LinearSVM svm;
svm.Lambda() = 0.1;

// Create AMSGrad optimizer with custom step size and batch size.
ens::AMSGrad optimizer(0.01 /* step size */, 16 /* batch size */);
optimizer.MaxIterations() = 100 * dataset.n_cols; // Allow 100 epochs.

// Print a progress bar and an optimization report when training is finished.
svm.Train(dataset, labels, 2, optimizer, ens::ProgressBar(), ens::Report());

// Now predict on test labels and compute accuracy.

// See
arma::mat testDataset;
mlpack::data::Load("satellite.test.csv", testDataset, true);
// See
arma::Row<size_t> testLabels;
mlpack::data::Load("satellite.test.labels.csv", testLabels, true);

std::cout << std::endl;
std::cout << "Accuracy on training set: "
    << svm.ComputeAccuracy(dataset, labels) << "\%." << std::endl;
std::cout << "Accuracy on test set:     "
    << svm.ComputeAccuracy(testDataset, testLabels) << "\%." << std::endl;

Train a linear SVM with SGD and save the model every epoch using a custom ensmallen callback:

// This callback saves the model into "model-<epoch>.bin" after every epoch.
class ModelCheckpoint
  ModelCheckpoint(mlpack::LinearSVM<>& model) : model(model) { }

  template<typename OptimizerType, typename FunctionType, typename MatType>
  bool EndEpoch(OptimizerType& /* optimizer */,
                FunctionType& /* function */,
                const MatType& /* coordinates */,
                const size_t epoch,
                const double /* objective */)
    const std::string filename = "model-" + std::to_string(epoch) + ".bin";
    mlpack::data::Save(filename, "svm", model, true);
    return false; // Do not terminate the optimization.

  mlpack::LinearSVM<>& model;

With that callback available, the code to train the model is below:

// See
arma::mat dataset;
mlpack::data::Load("satellite.train.csv", dataset, true);
// See
arma::Row<size_t> labels;
mlpack::data::Load("satellite.train.labels.csv", labels, true);

mlpack::LinearSVM svm;

// Create AdaDelta optimizer with a small step size and batch size of 1.
ens::AdaDelta adaDelta(0.001, 1);
adaDelta.MaxIterations() = 100 * dataset.n_cols; // 100 epochs maximum.

// Use the custom callback and an L2 penalty parameter of 0.01, with default
// delta and fitting an intercept.
svm.Train(dataset, labels, 2, adaDelta, 0.01, 1.0, true, ModelCheckpoint(svm),

// Now files like model-1.bin, model-2.bin, etc. should be saved on disk.

Load a linear SVM from disk and print some information about it.

mlpack::LinearSVM svm;
// This assumes that a model called "svm" has been saved to the file
// "model-1.bin" (as in the previous example).
mlpack::data::Load("model-1.bin", "svm", svm, true);

// Print the dimensionality of the model and some other statistics.
std::cout << "The dimensionality of the model in model-1.bin is "
    << svm.FeatureSize() << "." << std::endl;
if (svm.FitIntercept())
  std::cout << "Intercept values for each class: " << std::endl;
  for (size_t i = 0; i < svm.Parameters().n_cols; ++i)
    std::cout << "  - Class " << i << ": "
        << svm.Parameters()(svm.Parameters().n_rows - 1, i) << "." << std::endl;
  std::cout << "The model does not have an intercept fitted." << std::endl;

std::cout << "The L2 regularization penalty parameter is: " << svm.Lambda()
    << "." << std::endl;

std::cout << "Weights for the first dimension are: "
    << svm.Parameters().row(0);

🔗 Advanced Functionality: Different Element Types

The LinearSVM class has one template parameter that can be used to control the element type of the model. The full signature of the class is:


ModelMatType specifies the type of matrix used for training data and internal representation of model parameters.

The example below trains a linear SVM on sparse 32-bit floating point data, but uses dense 32-bit floating point matrices to store the model itself.

// Create random, sparse 100-dimensional data, with 3 classes.
arma::sp_fmat dataset;
dataset.sprandu(100, 5000, 0.3);
arma::Row<size_t> labels =
    arma::randi<arma::Row<size_t>>(5000, arma::distr_param(0, 2));

mlpack::LinearSVM<arma::fmat> svm(dataset, labels, 3);

// Now classify a test point.
arma::sp_fvec point;
point.sprandu(100, 1, 0.3);

size_t prediction;
arma::fvec probabilitiesVec;
svm.Classify(point, prediction, probabilitiesVec);

std::cout << "Prediction for random test point: " << prediction << "."
    << std::endl;
std::cout << "Class probabilities for random test point: "
    << probabilitiesVec.t();

Note: dense objects should be used for ModelMatType, since in general L2-regularized models are fully dense.