Principle Component Analysis

Principle Component Analysis (PCA) is a widely used statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components (or sometimes, principal modes of variation). PCA can be done by two methods:

• Eigenvalue decomposition of a data covariance (or cross-correlation)
• Singular Value Decomposition of a data

It is usually performed after normalizing (centering by the mean) the data matrix for each attribute.

In Harp-DAAL, we have two methods for computing PCA

SVD Based PCA

The input is a set of p-dimensional dense vectors, DAAL kernel invokes a SVD decomposition to find out $p_r$ principle directions (Eigenvectors) The details of SVD kernel by Intel DAAL is here.

Harp-DAAL provides distributed mode for SVD based PCA for dense input datasets.

Correleation Based PCA

The input is a $p\tims p$ correlation matrix, and the DAAL PCA kernel will find out the $p_r$ directions ¹. Details from Intel DAAL Documentation is here.

Harp-DAAL provides distributed mode for Correlation based PCA for both of dense and sparse (CSR format) input datasets.