Abstract

A new look on the principal component analysis has been presented. Firstly, a ge-ometric interpretation of determination coefficient was shown. In turn, the abilityto represent the analyzed data and their interdependencies in the form of easy-to-understand basic geometric structures was shown. As a result of the analysis ofthese structures it was proposed to enrich the classical PCA. In particular, it wasproposed a new criterion for the selection of important principal components anda new algorithm for clustering primary variables by their level of similarity to theprincipal components. Virtual and real data spaces, as well as tensor operationson data, have also been identified.The anisotropy of the data was identified too.