Contents

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 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 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)
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 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
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
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 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
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)

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

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)
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 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)
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)
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)
double bias

The bias. Default value: 0.0.

Getter & Setter
double get_bias() const
auto & set_bias(double 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 &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)
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)

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

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 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)
double bias

The bias. Default value: 0.0.

Getter & Setter
double get_bias() const
auto & set_bias(double 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)
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)

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 table &data

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

Getter & Setter
const table & get_data() const
auto & set_data(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)

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 &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)
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 &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)

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

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