Model-based clustering of categorical data based on the Hamming distance

2022/12/09 by Argiento, Raffaele, Filippi-Mazzola, Edoardo, Paci, Lucia · 1 citation
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2212.04746

Abstract

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components. Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches.

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