Support Vector Machine Classifier (SVM)#

Support Vector Machine (SVM) classification and regression are among popular algorithms. It belongs to a family of generalized linear classification problems.

Operation	Computational methods		Programming Interface
Training	SMO	Thunder	train(…)	train_input	train_result
Inference	SMO	Thunder	infer(…)	infer_input	infer_result

Mathematical formulation#

Refer to Developer Guide: Support Vector Machine Classifier.

Programming Interface#

All types and functions in this section are declared in the oneapi::dal::svm namespace and are available via inclusion of the oneapi/dal/algo/svm.hpp header file.

Descriptor#

template<typename Float = float, typename Method = method::by_default, typename Task = task::by_default, typename Kernel = linear_kernel::descriptor<Float>> class descriptor#

Template Parameters:

Float – The floating-point type that the algorithm uses for intermediate computations. Can be float or double.
Method – Tag-type that specifies an implementation of algorithm. Can be method::thunder or method::smo.
Task – Tag-type that specifies the type of the problem to solve. Can be task::classification, task::nu_classification, task::regression, or task::nu_regression.

Constructors

descriptor(const Kernel &kernel = kernel_t{})#: Creates a new instance of the class with the given descriptor of the kernel function.

Properties

std::int64_t max_iteration_count#

The maximum number of iterations \(T\). Default value: 100000.

Getter & Setter: std::int64_t get_max_iteration_count() const

auto & set_max_iteration_count(std::int64_t value)
Invariants: max_iteration_count >= 0

bool shrinking#

A flag that enables the use of a shrinking optimization technique. Used with method::smo split-finding method only. Default value: true.

Getter & Setter: bool get_shrinking() const

auto & set_shrinking(bool value)

std::int64_t class_count#

The number of classes. Used with task::classification and task::nu_classification. Default value: 2.

Getter & Setter: template <typename T = Task, typename None = detail::enable_if_classification_t<T>> std::int64_t get_class_count() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_class_count(std::int64_t value)
Invariants: class_count >= 2

double cache_size#

The size of cache (in megabytes) for storing the values of the kernel matrix. Default value: 200.0.

Getter & Setter: double get_cache_size() const

auto & set_cache_size(double value)
Invariants: cache_size >= 0.0

double tau#

The threshold parameter \(\tau\) for computing the quadratic coefficient. Default value: 1e-6.

Getter & Setter: double get_tau() const

auto & set_tau(double value)
Invariants: tau > 0.0

double nu#

The nu. Used with task::nu_classification and task::nu_regression. Default value: 0.5.

Getter & Setter: template <typename T = Task, typename None = detail::enable_if_nu_task_t<T>> double get_nu() const

template <typename T = Task, typename None = detail::enable_if_nu_task_t<T>> auto & set_nu(double value)
Invariants: 0 < nu <= 1

double epsilon#

The epsilon. Used with task::regression only. Default value: 0.1.

Getter & Setter: template <typename T = Task, typename None = detail::enable_if_epsilon_available_t<T>> double get_epsilon() const

template <typename T = Task, typename None = detail::enable_if_epsilon_available_t<T>> auto & set_epsilon(double value)
Invariants: epsilon >= 0

double accuracy_threshold#

The threshold \(\varepsilon\) for the stop condition. Default value: 0.0.

Getter & Setter: double get_accuracy_threshold() const

auto & set_accuracy_threshold(double value)
Invariants: accuracy_threshold >= 0.0

double c#

The upper bound \(C\) in constraints of the quadratic optimization problem. Used with task::classification, task::regression, and task::nu_regression. Default value: 1.0.

Getter & Setter: template <typename T = Task, typename None = detail::enable_if_c_available_t<T>> double get_c() const

template <typename T = Task, typename None = detail::enable_if_c_available_t<T>> auto & set_c(double value)
Invariants: c > 0

const Kernel &kernel#

The descriptor of kernel function \(K(x, y)\). Can be linear_kernel::descriptor or polynomial_kernel::descriptor or rbf_kernel::descriptor or sigmoid_kernel::descriptor.

Getter & Setter: const Kernel & get_kernel() const

auto & set_kernel(const Kernel &kernel)

Method tags#

struct smo#: Tag-type that denotes SMO computational method.

struct thunder#: Tag-type that denotes Thunder computational method.

using by_default = thunder #: Alias tag-type for Thunder computational method.

Task tags#

struct classification#: Tag-type that parameterizes entities that are used for solving classification problem.

struct nu_classification#: Tag-type that parameterizes entities that are used for solving nu-classification problem.

struct nu_regression#: Tag-type that parameterizes entities used for solving nu-regression problem.

struct regression#: Tag-type that parameterizes entities used for solving regression problem.

using by_default = classification #: Alias tag-type for classification task.

Model#

template<typename Task = task::by_default> class model#

Template Parameters:: Task – Tag-type that specifies the type of the problem to solve. Can be task::classification, task::nu_classification, task::regression, or task::nu_regression.

Constructors

model()#: Creates a new instance of the class with the default property values.

Public Methods

std::int64_t get_support_vector_count() const#: The number of support vectors.

Properties

double bias#

The bias. Default value: 0.0.

Getter & Setter: double get_bias() const

auto & set_bias(double value)

std::int64_t second_class_response#

The second unique value in class responses. Used with task::classification and task::nu_classification.

Getter & Setter: std::int64_t get_second_class_response() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_second_class_response(std::int64_t value)

const table &biases#

A \(class_count*(class_count-1)/2 \times 1\) table for task::classification and task::nu_classification and a \(1 \times 1\) table for task::regression and task::nu_regression containing constants in decision function.

Getter & Setter: const table & get_biases() const

auto & set_biases(const table &value)

std::int64_t first_class_response#

The first unique value in class responses. Used with task::classification and task::nu_classification.

Getter & Setter: std::int64_t get_first_class_response() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_first_class_response(std::int64_t value)

std::int64_t second_class_label#

The second unique value in class labels. Used with task::classification and task::nu_classification.

Getter & Setter: std::int64_t get_second_class_label() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_second_class_label(std::int64_t value)

const table &coeffs#

A \(nsv \times class_count - 1\) table for task::classification and task::nu_classification and a \(nsv \times 1\) table for task::regression and task::nu_regression containing coefficients of Lagrange multiplier. Default value: table{}.

Getter & Setter: const table & get_coeffs() const

auto & set_coeffs(const table &value)

std::int64_t first_class_label#

The first unique value in class labels. Used with task::classification and task::nu_classification.

Getter & Setter: std::int64_t get_first_class_label() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_first_class_label(std::int64_t value)

const table &support_vectors#

A \(nsv \times p\) table containing support vectors. Where \(nsv\) - number of support vectors. Default value: table{}.

Getter & Setter: const table & get_support_vectors() const

auto & set_support_vectors(const table &value)

Training train(...)#

Input#

template<typename Task = task::by_default> class train_input#

Template Parameters:: Task – Tag-type that specifies the type of the problem to solve. Can be oneapi::dal::svm::task::classification, oneapi::dal::svm::task::nu_classification, oneapi::dal::svm::task::regression, or oneapi::dal::svm::task::nu_regression.

Constructors

train_input(const table &data, const table &responses, const table &weights = table{})#: Creates a new instance of the class with the given data, responses and weights.

Properties

const table &responses#

The vector of responses \(y\) for the training set \(X\). Default value: table{}.

Getter & Setter: const table & get_responses() const

auto & set_responses(const table &value)

const table &labels#

The vector of labels \(y\) for the training set \(X\). Default value: table{}.

Getter & Setter: const table & get_labels() const

auto & set_labels(const table &value)

const table &weights#

The vector of weights \(w\) for the training set \(X\). Default value: table{}.

Getter & Setter: const table & get_weights() const

auto & set_weights(const table &value)

const table &data#

The training set \(X\). Default value: table{}.

Getter & Setter: const table & get_data() const

auto & set_data(const table &value)

Result#

template<typename Task = task::by_default> class train_result#

Template Parameters:: Task – Tag-type that specifies the type of the problem to solve. Can be oneapi::dal::svm::task::classification, oneapi::dal::svm::task::nu_classification, oneapi::dal::svm::task::regression, or oneapi::dal::svm::task::nu_regression.

Constructors

train_result()#: Creates a new instance of the class with the default property values.

Public Methods

std::int64_t get_support_vector_count() const#: The number of support vectors.

Properties

double bias#

The bias. Default value: 0.0.

Getter & Setter: double get_bias() const

auto & set_bias(double value)

const table &support_indices#

A \(nsv \times 1\) table containing support indices. Default value: table{}.

Getter & Setter: const table & get_support_indices() const

auto & set_support_indices(const table &value)

const table &biases#

A \(class_count*(class_count-1)/2 \times 1\) table for task::classification and task::classification and \(1 \times 1\) table for task::regression and task::nu_regression containing constants in decision function.

Getter & Setter: const table & get_biases() const

auto & set_biases(const table &value)

const table &coeffs#

A \(nsv \times class_count - 1\) table for task::classification and task::classification and \(nsv \times 1\) table for task::regression and task::nu_regression containing coefficients of Lagrange multiplier. Default value: table{}.

Getter & Setter: const table & get_coeffs() const

auto & set_coeffs(const table &value)

const model<Task> &model#

The trained SVM model. Default value: model<Task>{}.

Getter & Setter: const model< Task > & get_model() const

auto & set_model(const model< Task > &value)

const table &support_vectors#

A \(nsv \times p\) table containing support vectors, where \(nsv\) is the number of support vectors. Default value: table{}.

Getter & Setter: const table & get_support_vectors() const

auto & set_support_vectors(const table &value)

Operation#

template<typename Descriptor> svm::train_result train(const Descriptor &desc, const svm::train_input &input)#

Parameters:

desc – SVM algorithm descriptor svm::descriptor.
input – Input data for the training operation

Preconditions: input.data.is_empty == false

input.labels.is_empty == false

input.labels.column_count == 1

input.data.row_count == input.labels.row_count

Inference infer(...)#

Input#

template<typename Task = task::by_default> class infer_input#

Template Parameters:: Task – Tag-type that specifies the type of the problem to solve. Can be oneapi::dal::svm::task::classification, oneapi::dal::svm::task::nu_classification, oneapi::dal::svm::task::regression, or oneapi::dal::svm::task::nu_regression.

Constructors

infer_input(const model<Task> &trained_model, const table &data)#: Creates a new instance of the class with the given model and data property values.

Properties

const model<Task> &model#

The trained SVM model. Default value: model<Task>{}.

Getter & Setter: const model< Task > & get_model() const

auto & set_model(const model< Task > &value)

const table &data#

The dataset for inference \(X'\). Default value: table{}.

Getter & Setter: const table & get_data() const

auto & set_data(const table &value)

Result#

template<typename Task = task::by_default> class infer_result#

Template Parameters:: Task – Tag-type that specifies the type of the problem to solve. Can be oneapi::dal::svm::task::classification, oneapi::dal::svm::task::nu_classification, oneapi::dal::svm::task::regression, or oneapi::dal::svm::task::nu_regression.

Constructors

infer_result()#: Creates a new instance of the class with the default property values.

Properties

const table &decision_function#

The \(n \times 1\) table with the predicted class. Used with oneapi::dal::svm::task::classification and oneapi::dal::svm::task::nu_classification. decision function for each observation. Default value: table{}.

Getter & Setter: const table & get_decision_function() const

template <typename T = Task, typename None = detail::enable_if_classification_t<T>> auto & set_decision_function(const table &value)

const table &responses#

The \(n \times 1\) table with the predicted responses. Default value: table{}.

Getter & Setter: const table & get_responses() const

auto & set_responses(const table &value)

const table &labels#

The \(n \times 1\) table with the predicted labels. Default value: table{}.

Getter & Setter: const table & get_labels() const

auto & set_labels(const table &value)

Operation#

template<typename Descriptor> svm::infer_result infer(const Descriptor &desc, const svm::infer_input &input)#

Parameters:

desc – SVM algorithm descriptor svm::descriptor.
input – Input data for the inference operation

Preconditions: input.data.is_empty == false

Examples#

Batch Processing:

svm_two_class_thunder_dense_batch.cpp

Support Vector Machine Classifier (SVM)

Contents

Support Vector Machine Classifier (SVM)#

Mathematical formulation#

Programming Interface#

Descriptor#

Method tags#

Task tags#

Model#

Training train(...)#

Input#

Result#

Operation#

Inference infer(...)#

Input#

Result#

Operation#

Examples#