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

Raffaele Argiento; Edoardo Filippi-Mazzola; Lucia Paci

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arXiv · 2212.04746

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

Raffaele Argiento·Edoardo Filippi-Mazzola·Lucia Paci

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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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BibTeX RIS

Raffaele Argiento, Edoardo Filippi-Mazzola, Lucia Paci. 2022-12-09. Model-based clustering of categorical data based on the Hamming distance. https://arxiv.org/abs/2212.04746

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