Principal Component Analysis - Computing PCA Using The Covariance Method

Computing PCA Using The Covariance Method

The following is a detailed description of PCA using the covariance method (see also here). But note that it is better to use the singular value decomposition (using standard software).

The goal is to transform a given data set X of dimension M to an alternative data set Y of smaller dimension L. Equivalently, we are seeking to find the matrix Y, where Y is the Karhunen–Loève transform (KLT) of matrix X: