Comparing Interpoint Distances in Correspondence Analysis: A Clarification

In a recent JMR article, the authors described and illustrated a correspondence analysis scaling that permitted both within-set and between-set squared distance comparisons. This note clarifies the relationship between the proposed scaling and another scaling (popular among the “French school” of data analysts) in which the diagonal matrix of singular values is applied to both X and Y coordinates. Using a data set from Greenacre, the authors examine conceptual and empirical contrasts among three alternative scalings.