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

• 成果类型: Article
• 署名作者: Argiento, Raffaele; Filippi-Mazzola, Edoardo; Paci, Lucia
• 署名单位: University of Bergamo; Universita della Svizzera Italiana; Catholic University of the Sacred Heart
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2402568
• 发表日期: 2025
• 页码: 1178-1188
• 关键词: posterior distribution; mixture; Finite; Identifiability; INFINITY; number

摘要

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.