Some new aspects of taxicab correspondence analysis

Correspondence analysis (CA) and nonsymmetric correspondence analysis are based on generalized singular value decomposition, and, in general, they are not equivalent. Taxicab correspondence analysis (TCA) is a L1 variant of CA, and it is based on the generalized taxicab singular value decomposition (GTSVD). Our aim is to study the taxicab variant of nonsymmetric correspondence analysis. We find that for diagonal metric matrices GTSVDs of a given data set are equivalent; from which we deduce the equivalence of TCA and taxicab nonsymmetric correspondence analysis. We also attempt to show that TCA stays as close as possible to the original correspondence matrix without calculating a dissimilarity (or similarity) measure between rows or columns. Further, we discuss some new geometric and distance aspects of TCA.