Cluster Correspondence Analysis.

A method is proposed that combines dimension reduction and cluster analysis for categorical data by simultaneously assigning individuals to clusters and optimal scaling values to categories in such a way that a single between variance maximization objective is achieved. In a unified framework, a brief review of alternative methods is provided and we show that the proposed method is equivalent to GROUPALS applied to categorical data. Performance of the methods is appraised by means of a simulation study. The results of the joint dimension reduction and clustering methods are compared with the so-called tandem approach, a sequential analysis of dimension reduction followed by cluster analysis. The tandem approach is conjectured to perform worse when variables are added that are unrelated to the cluster structure. Our simulation study confirms this conjecture. Moreover, the results of the simulation study indicate that the proposed method also consistently outperforms alternative joint dimension reduction and clustering methods.