Visible to Intel only — GUID: GUID-95277FD5-A4E4-4996-A42D-B5FFEF7BFF12
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
cor_dense_batch.cpp
cov_dense_batch.cpp
dbscan_brute_force_batch.cpp
df_cls_hist_batch.cpp
df_cls_hist_batch_random.cpp
df_cls_traverse_model.cpp
df_reg_hist_batch.cpp
df_reg_hist_batch_random.cpp
df_reg_traverse_model.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_reg_brute_force_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
pca_cor_dense_batch.cpp
pca_precomputed_cor_dense_batch.cpp
pca_precomputed_cov_dense_batch.cpp
rbf_kernel_dense_batch.cpp
svm_two_class_thunder_dense_batch.cpp
basic_statistics_dense_batch.cpp
column_accessor_homogen.cpp
connected_components_batch.cpp
cor_dense_batch.cpp
cov_dense_batch.cpp
csr_accessor.cpp
dbscan_brute_force_batch.cpp
df_cls_dense_batch.cpp
df_reg_dense_batch.cpp
directed_graph.cpp
graph_service_functions.cpp
jaccard_batch.cpp
jaccard_batch_app.cpp
kmeans_init_dense.cpp
kmeans_lloyd_dense_batch.cpp
knn_cls_brute_force_dense_batch.cpp
knn_cls_kd_tree_dense_batch.cpp
knn_search_brute_force_dense_batch.cpp
linear_kernel_dense_batch.cpp
linear_regression_dense_batch.cpp
logloss_dense_batch.cpp
louvain_batch.cpp
pca_dense_batch.cpp
pca_precomputed_dense_batch.cpp
polynomial_kernel_dense_batch.cpp
rbf_kernel_dense_batch.cpp
shortest_paths_batch.cpp
sigmoid_kernel_dense_batch.cpp
subgraph_isomorphism_batch.cpp
svm_multi_class_thunder_csr_batch.cpp
svm_multi_class_thunder_dense_batch.cpp
svm_nu_cls_thunder_csr_batch.cpp
svm_nu_cls_thunder_dense_batch.cpp
svm_nu_reg_thunder_csr_batch.cpp
svm_nu_reg_thunder_dense_batch.cpp
svm_reg_thunder_csr_batch.cpp
svm_reg_thunder_dense_batch.cpp
svm_two_class_smo_csr_batch.cpp
svm_two_class_smo_dense_batch.cpp
svm_two_class_thunder_csr_batch.cpp
svm_two_class_thunder_dense_batch.cpp
triangle_counting_batch.cpp
Mathematical Notations
Mathematical Notations
Correlation and Variance-Covariance Matrices
Mathematical Notations
Principal Components Analysis Transform
Singular Value Decomposition
Association Rules
Mathematical Notations
Mathematical Notations
Cholesky Decomposition
QR Decomposition
Outlier Detection
Distance Matrix
Distributions
Engines
Moments of Low Order
Mathematical Notations
Quality Metrics
Sorting
Normalization
Mathematical Notations
Visible to Intel only — GUID: GUID-95277FD5-A4E4-4996-A42D-B5FFEF7BFF12
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 |
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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: