Visible to Intel only — GUID: GUID-C85C82DF-009B-4E61-B7BD-1B6F920EA9F3
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_traverse_model.cpp
df_reg_hist_batch.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
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
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_dense_batch.cpp
svm_nu_cls_thunder_dense_batch.cpp
svm_nu_reg_thunder_dense_batch.cpp
svm_reg_thunder_dense_batch.cpp
svm_two_class_smo_dense_batch.cpp
svm_two_class_thunder_dense_batch.cpp
triangle_counting_batch.cpp
K-Means Clustering
Density-Based Spatial Clustering of Applications with Noise
Correlation and Variance-Covariance Matrices
Principal Component Analysis
Details
Computation
Examples
Performance Considerations
Principal Components Analysis Transform
Singular Value Decomposition
Association Rules
Kernel Functions
Expectation-Maximization
Cholesky Decomposition
QR Decomposition
Outlier Detection
Distance Matrix
Distributions
Engines
Moments of Low Order
Quantile
Quality Metrics
Sorting
Normalization
Optimization Solvers
Decision Forest
Decision Trees
Gradient Boosted Trees
Stump
Linear and Ridge Regressions
LASSO and Elastic Net Regressions
k-Nearest Neighbors (kNN) Classifier
Implicit Alternating Least Squares
Logistic Regression
Naïve Bayes Classifier
Support Vector Machine Classifier
Multi-class Classifier
Boosting
Visible to Intel only — GUID: GUID-C85C82DF-009B-4E61-B7BD-1B6F920EA9F3
Principal Component Analysis
NOTE:
Principal Component Analysis is also available with oneAPI interfaces:
Principal Component Analysis (PCA) is a method for exploratory data analysis. PCA transforms a set of observations of possibly correlated variables to a new set of uncorrelated variables, called principal components. Principal components are the directions of the largest variance, that is, the directions where the data is mostly spread out.
Because all principal components are orthogonal to each other, there is no redundant information. This is a way of replacing a group of variables with a smaller set of new variables. PCA is one of powerful techniques for dimension reduction.
Details
Given a set 
of p-dimensional feature vectors or a 
correlation matrix and the number of principal components 
, the problem is to compute principal directions (eigenvectors) for the data set. The library returns the transformation matrix T of size 
, which contains eigenvectors in the row-major order and a vector of respective eigenvalues in descending order.
oneDAL provides two methods for running PCA:
SVD
Correlation
Eigenvectors computed by PCA are not uniquely defined due to sign ambiguity. PCA supports fast ad-hoc “sign flip” technique described in the paper [Bro07]. It modifies the signs of eigenvectors shown below:
where T-transformation matrix is computed by PCA, 
- i-th row in the matrix, j - column number, sgn - signum function:
You can provide these types of input data to the PCA algorithms of the library:
Original, non-normalized data set
Normalized data set, where each feature has the zero mean and unit variance
Correlation matrix
Computation
The following computation modes are available:
Examples
oneAPI DPC++
Batch Processing:
dpc_pca_cor_dense_batch.cpp
oneAPI C++
Batch Processing:
cpp_pca_dense_batch.cpp
C++ (CPU)
Batch Processing:
Online Processing:
Distributed Processing:
Java*
NOTE:
There is no support for Java on GPU.
Batch Processing:
Online Processing:
Distributed Processing:
Python* with DPC++ support
Batch Processing:
Python*
Batch Processing:
Distributed Processing:
Performance Considerations
To get the best overall performance of the PCA algorithm:
If input data is homogeneous, provide the input data and store results in homogeneous numeric tables of the same type as specified in the algorithmFPType class template parameter.
If input data is non-homogeneous, use AOS layout rather than SOA layout.
PCA computation using the correlation method involves the correlation and variance-covariance matrices algorithm. Depending on the method of this algorithm, the performance of PCA computations may vary. For sparse data sets, use the methods of this algorithm for sparse data.
Batch Processing
Because the PCA in the batch processing mode performs normalization for data passed as Input ID, to achieve the best performance, normalize the input data set. To inform the algorithm that the data is normalized, set the normalization flag for the input numeric table that represents your data set by calling the setNormalizationFlag() method of the NumericTableIface class.
Because the PCA with the correlation method (defaultDense) in the batch processing mode is based on the computation of the correlation matrix, to achieve the best performance, precompute the correlation matrix. To pass the precomputed correlation matrix to the algorithm, use correlation as Input ID.
Online Processing
PCA with the SVD method (svdDense) in the online processing mode is at least as computationally complex as in the batch processing mode and has high memory requirements for storing auxiliary data between calls to compute(). On the other hand, the online version of the PCA with the SVD method may enable you to hide the latency of reading data from a slow data source. To do this, implement load prefetching of the next data block in parallel with the compute() method for the current block.
Distributed Processing
PCA with the SVD method (svdDense) in the distributed processing mode requires gathering local-node numeric tables on the master node. When the amount of local-node work is small, that is, when the local-node data set is small, the network data transfer may become a bottleneck. To avoid this situation, ensure that local nodes have a sufficient amount of work. For example, distribute the input data set across a smaller number of nodes.
Product and Performance Information |
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Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201 |