Model-Based Clustering of Categorical Data Based on the Hamming Distance

Raffaele Argiento, Edoardo Filippi-Mazzola and Lucia Paci

Journal of the American Statistical Association, 2025, vol. 120, issue 550, 1178-1188

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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Date: 2025
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DOI: 10.1080/01621459.2024.2402568

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