Multiple Correspondence K-Means: Simultaneous Versus Sequential Approach for Dimension Reduction and Clustering

In this work, a discrete model for clustering and a continuous factorial one for dimension reduction are simultaneously fitted to categorical data, with the aim of identifying the best partition of the objects, described by the best orthogonal linear combinations of the factors, according to the least-squares criterion. This new methodology named multiple correspondence k-means is a useful alternative to the Tandem Analysis in the case of categorical data. Then, this approach has a double objective: data reduction and synthesis, simultaneously in the direction of rows and columns of the data matrix.