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 |
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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, typenameMethod
= method::by_default, typenameTask
= task::by_default, typenameKernel
= linear_kernel::descriptor<Float>>
classdescriptor
¶ - Template Parameters
Float – The floating-point type that the algorithm uses for intermediate computations. Can be
float
ordouble
.Method – Tag-type that specifies an implementation of algorithm. Can be
method::thunder
ormethod::smo
.Task – Tag-type that specifies the type of the problem to solve. Can be
task::classification
,task::nu_classification
,task::regression
, ortask::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
andtask::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
, andtask::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
orpolynomial_kernel::descriptor
orrbf_kernel::descriptor
orsigmoid_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
andtask::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
Method tags¶
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>
classmodel
¶ - Template Parameters
Task – Tag-type that specifies the type of the problem to solve. Can be
task::classification
,task::nu_classification
,task::regression
, ortask::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
andtask::nu_classification
and a \(1 \times 1\) table fortask::regression
andtask::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
andtask::nu_classification
and a \(nsv \times 1\) table fortask::regression
andtask::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
andtask::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
andtask::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
andtask::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
andtask::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>
classtrain_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
, oroneapi::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
andweights
.
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)
Result¶
-
template<typename
Task
= task::by_default>
classtrain_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
, oroneapi::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
andtask::classification
and \(1 \times 1\) table fortask::regression
andtask::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
andtask::classification
and \(nsv \times 1\) table fortask::regression
andtask::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)
Operation¶
-
template<typename
Descriptor
>
svm::train_resulttrain
(const Descriptor &desc, const svm::train_input &input)¶ - Parameters
desc – SVM algorithm descriptor
svm::descriptor
.input – Input data for the training operation
- Preconditions
Inference infer(...)
¶
Input¶
-
template<typename
Task
= task::by_default>
classinfer_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
, oroneapi::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
anddata
property values.
Properties
Result¶
-
template<typename
Task
= task::by_default>
classinfer_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
, oroneapi::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
andoneapi::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_resultinfer
(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:
Batch Processing:
Batch Processing: