Principal Component Analysis versus Factor Analysis

TL;DR

This paper compares principal component analysis and factor analysis, proposing new criteria and algorithms for determining their number of components, with a focus on maximizing variance representation.

Contribution

It introduces a new criterion and efficient algorithms for selecting the number of components in PCA and FA, enhancing variance explanation.

Findings

New criterion for component determination

Efficient algorithms for PCA and FA

Improved variance coverage in analysis

Abstract

The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed. The problem of determining the number of principal components in PCA and factors in FA was discussed in detail. A new criterion for determining the number of factors and principal components is discussed, which will allow to present most of the variance of each of the analyzed primary variables. An efficient algorithm for determining the number of factors in FA, which complies with this criterion, was also proposed. This algorithm was adapted to find the number of principal components in PCA. It was also proposed to modify the PCA algorithm using a new method of determining the number of principal components. The obtained results were discussed.