Clustering and Model Selection via Penalized Likelihood for Different-sized Categorical Data Vectors

TL;DR

This paper introduces a penalized likelihood approach for clustering categorical data vectors of varying sizes, providing theoretical guarantees and a robust EM algorithm, demonstrated through document clustering.

Contribution

It develops a new penalized likelihood method with theoretical oracle inequalities for clustering heterogeneous categorical data, including a novel robust EM algorithm.

Findings

The method achieves non-asymptotic oracle inequalities.

The robust EM algorithm effectively estimates mixture parameters.

Application to document clustering demonstrates practical utility.

Abstract

In this study, we consider unsupervised clustering of categorical vectors that can be of different size using mixture. We use likelihood maximization to estimate the parameters of the underlying mixture model and a penalization technique to select the number of mixture components. Regardless of the true distribution that generated the data, we show that an explicit penalty, known up to a multiplicative constant, leads to a non-asymptotic oracle inequality with the Kullback-Leibler divergence on the two sides of the inequality. This theoretical result is illustrated by a document clustering application. To this aim a novel robust expectation-maximization algorithm is proposed to estimate the mixture parameters that best represent the different topics. Slope heuristics are used to calibrate the penalty and to select a number of clusters.