Developer Guide for Intel® Data Analytics Acceleration Library 2018

Quality Metrics for Principal Components Analysis

Given the results of the PCA algorithm, data set E = (e i ), i = 1, ..., p of eigenvalues in decreasing order, full number of principal components p and reduced number of components p r p the problem is to evaluate the explained variances radio and noise variance.

The metrics are computed given the input data meets the following requirements:

The PCA quality metrics include:

The library uses the following quality metrics:

Quality Metric

Definition

Explained variance

Eigenvalues:

Explained variance ratios



Noise variance



p r - number of principal components, p - number of features in the data set

Note

You can use quality metrics for the PCA algorithm only when . Otherwise, it returns the error.