ABSTRACT
So far CA has been presented as a geometric method of data analysis, stressing the three basic concepts of profile, mass and χ2-distance, and the four derived concepts of centroid (weighted average), inertia, subspace and projection. Profiles are multidimensional points, weighted by masses, and distances between profiles are measured using the χ2-distance. The profiles are visualized by projecting them onto a subspace of low dimensionality which best fits the profiles, and then projecting the vertex profiles onto the subspace as reference points for the interpretation. There are, however, numerous other ways to define and interpret CA and this is why the same underlying methodology has been rediscovered many times in different contexts. One of these alternative interpretations is called optimal scaling and a discussion of this approach at this point will provide additional insight into the properties of CA.
