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

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 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

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

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 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 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 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

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 &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)

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)

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)

double bias¶

The bias. Default value: 0.0.

Getter & Setter: double get_bias() const

auto & set_bias(double 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 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)

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 &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 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)

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)

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 &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)

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 Machines

Distributed Model: Single Process Multiple Data

oneDAL documentation

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¶