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New Interpretation of Principal Components Analysis

Gniazdowski Z.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

2017

nr 16

43--65

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