A generalization of principal component analysis to K sets of variables

摘要

The aim of this paper is to introduce a new method, generalized principal component analysis (GPCA), which is a generalization of principal component analysis (PCA), to several data tables. GPCA is a method for both finding common dimensions in several sets of variables and giving a description of each set of variables: GPCA takes into account both the correlation structure within sets and relationships between sets. Two sorts of orthogonal basis are provided; the fist basis is useful to represent each set of variables (as PCA does) and the second is useful to represent associations between sets of variables (as canonical correlation analysis does). An example using real data (evolution of five characteristics of car markets from 86 to 93 for 8 countries) illustrates the method.