Clustering criteria for discrete data and latent class models

Abstract

We show that a well-known clustering criterion for discrete data, the information criterion, is closely related to the classification maximum likelihood criterion for the latent class model. This relation can be derived from the Bryant-Windham construction. Emphasis is placed on binary clustering criteria which are analyzed under the maximum likelihood approach for different multivariate Bernoulli mixtures. This alternative form of criterion reveals non-apparent aspects of clustering techniques. All the criteria discussed can be optimized with the alternating optimization algorithm. Some illustrative applications are included.