Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis

Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after other. The accepted criterion evaluating Component’s (PC) performance λ_j/tr(S) where tr(S) denotes trace covariance matrix S. standard procedure to determine how many PCs should be maintained using predetermined percentage total variance. In study, diagonal elements are used instead eigenvalues need considered obtain defined threshold For this, an approach which uses important theorems majorization theory proposed. Based on tests, lowers computational costs.