Intel® oneAPI Data Analytics Library Developer Guide and Reference
A newer version of this document is available. Customers should click here to go to the newest version.
Principal Components Analysis (PCA)
Principal Component Analysis (PCA) is an algorithm for exploratory data analysis and dimensionality reduction. PCA transforms a set of feature vectors of possibly correlated features to a new set of uncorrelated features, called principal components. Principal components are the directions of the largest variance, that is, the directions where the data is mostly spread out.
Operation |
Computational methods |
Programming Interface |
|||
Mathematical formulation
Programming Interface
All types and functions in this section are declared in the oneapi::dal::pca namespace and be available via inclusion of the oneapi/dal/algo/pca.hpp header file.
Descriptor
template<typenameFloat=float,typenameMethod=method::by_default,typenameTask=task::by_default>classdescriptor
- 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::cov or method::svd.
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
descriptor(std::int64_tcomponent_count=0)
Creates a new instance of the class with the given component_count property value.
Properties
booldeterministic
Specifies whether the algorithm applies the sign-flip technique. If it is true, the directions of the eigenvectors must be deterministic. Default value: true.
- Getter & Setter
-
bool get_deterministic() const
auto & set_deterministic(bool value)
std::int64_tcomponent_count
The number of principal components \(r\). If it is zero, the algorithm computes the eigenvectors for all features, \(r = p\). Default value: 0.
- Getter & Setter
-
std::int64_t get_component_count() const
auto & set_component_count(std::int64_t value)
- Invariants
-
component_count >= 0
result_option_idresult_options
Choose which results should be computed and returned.
- Getter & Setter
-
result_option_id get_result_options() const
auto & set_result_options(const result_option_id &value)
Method tags
structcov
Tag-type that denotes Covariance computational method.
structprecomputed
structsvd
Tag-type that denotes SVD computational method.
usingby_default=cov
Alias tag-type for Covariance computational method.
Task tags
structdim_reduction
Tag-type that parameterizes entities used for solving dimensionality reduction problem.
usingby_default=dim_reduction
Alias tag-type for dimensionality reduction task.
Model
template<typenameTask=task::by_default>classmodel
- Template Parameters
-
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
model()
Creates a new instance of the class with the default property values.
Properties
consttable&eigenvectors
An \(r \times p\) table with the eigenvectors. Each row contains one eigenvector. Default value: table{}.
- Getter & Setter
-
const table & get_eigenvectors() const
auto & set_eigenvectors(const table &value)
Training train(...)
Input
template<typenameTask=task::by_default>classtrain_input
- Template Parameters
-
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
train_input(consttable&data)
Creates a new instance of the class with the given data property value.
Properties
consttable&data
An \(n \times p\) table with the training data, where each row stores one feature vector. Default value: table{}.
- Getter & Setter
-
const table & get_data() const
auto & set_data(const table &data)
Result
template<typenameTask=task::by_default>classtrain_result
- Template Parameters
-
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
train_result()
Creates a new instance of the class with the default property values.
Public Methods
consttable&get_eigenvectors()const
An \(r \times p\) table with the eigenvectors. Each row contains one eigenvector.
Properties
consttable&means
A \(1 \times r\) table that contains the mean values for the first r features. Default value: table{}.
- Getter & Setter
-
const table & get_means() const
auto & set_means(const table &value)
consttable&eigenvalues
A \(1 \times r\) table that contains the eigenvalues for for the first r features. Default value: table{}.
- Getter & Setter
-
const table & get_eigenvalues() const
auto & set_eigenvalues(const table &value)
consttable&variances
A \(1 \times r\) table that contains the variances for the first r features. Default value: table{}.
- Getter & Setter
-
const table & get_variances() const
auto & set_variances(const table &value)
constmodel<Task>&model
The trained PCA model. Default value: model<Task>{}.
- Getter & Setter
-
const model< Task > & get_model() const
auto & set_model(const model< Task > &value)
constresult_option_id&result_options
Result options that indicates availability of the properties. Default value: default_result_options<Task>.
- Getter & Setter
-
const result_option_id & get_result_options() const
auto & set_result_options(const result_option_id &value)
Operation
template<typenameDescriptor>pca::train_resulttrain(constDescriptor&desc, constpca::train_input&input)
- Parameters
-
desc – PCA algorithm descriptor pca::descriptor
input – Input data for the training operation
- Preconditions
-
input.data.has_data == true
input.data.column_count >= desc.component_count
- Postconditions
-
result.means.row_count == 1
result.means.column_count == desc.component_count
result.variances.row_count == 1
result.variances.column_count == desc.component_count
result.variances[i] >= 0.0
result.eigenvalues.row_count == 1
result.eigenvalues.column_count == desc.component_count
result.model.eigenvectors.row_count == 1
result.model.eigenvectors.column_count == desc.component_count
Inference infer(...)
Input
template<typenameTask=task::by_default>classinfer_input
- Template Parameters
-
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
infer_input(constmodel<Task>&trained_model, consttable&data)
Creates a new instance of the class with the given model and data property values.
Properties
constmodel<Task>&model
The trained PCA model. Default value: model<Task>{}.
- Getter & Setter
-
const model< Task > & get_model() const
auto & set_model(const model< Task > &value)
consttable&data
The dataset for inference \(X'\). Default value: table{}.
- Getter & Setter
-
const table & get_data() const
auto & set_data(const table &value)
Result
template<typenameTask=task::by_default>classinfer_result
- Template Parameters
-
Task – Tag-type that specifies type of the problem to solve. Can be task::dim_reduction.
Constructors
infer_result()
Creates a new instance of the class with the default property values.
Properties
consttable&transformed_data
An \(n \times r\) table that contains data projected to the r principal components. Default value: table{}.
- Getter & Setter
-
const table & get_transformed_data() const
auto & set_transformed_data(const table &value)
Operation
template<typenameDescriptor>pca::infer_resultinfer(constDescriptor&desc, constpca::infer_input&input)
- Parameters
-
desc – PCA algorithm descriptor pca::descriptor
input – Input data for the inference operation
Usage example
Training
pca::model<> run_training(const table& data) {
const auto pca_desc = pca::descriptor<float>{}
.set_component_count(5)
.set_deterministic(true);
const auto result = train(pca_desc, data);
print_table("means", result.get_means());
print_table("variances", result.get_variances());
print_table("eigenvalues", result.get_eigenvalues());
print_table("eigenvectors", result.get_eigenvectors());
return result.get_model();
}
Inference
table run_inference(const pca::model<>& model,
const table& new_data) {
const auto pca_desc = pca::descriptor<float>{}
.set_component_count(model.get_component_count());
const auto result = infer(pca_desc, model, new_data);
print_table("labels", result.get_transformed_data());
}
Examples
oneAPI DPC++
Batch Processing:
oneAPI C++
Batch Processing:
Python* with DPC++ support
Batch Processing: