On detrending in correspondence analysis and principal component analysis

Abstract

Both correspondence analysis (CA) and principal components analysis (PCA) may generate either 'arch' or 'horseshoe' effect. In this paper I review the methods that attenuate these undesirable effects, and consequently improve CA and PCA. Detrending methods (detrending by segments and detrending by polynomials) reduce the arch, but not the horseshoe effect. In contrast, the generalized standardization procedure (GSP) is able to unfold involuted ends of a coenospace and thus eliminate the horseshoe effect. This method significantly improves PCA but not CA, since CA is insensitive to GSP.