A Comparison between Principal Component Analysis and Factor Analysis

The principal component analysis (also named Karhunen–Loève transformation) and the factor analysis are both tools of the multivariate statistics, more precisely the exploratory data analysis. They are used e.g. in data mining or machine learning. Although they share the same goal, they reach it with different methods. Over the years, some misunderstandings came up, how these methods differ from each other. The result is, that sometimes if one talks about using the factor analysis, actually the principal component analysis was implemented. Or it is believed, that the factor analysis is an superset of the principal component analysis. These misconceptions could prevent practitioners to chose the appropriate tool for their intended use. This paper clarifies some misconceptions. After some introductory words, principal component analysis and factor analysis are described on its own. This lays the foundation of a comparison between them. The conclusion settles the case.