A New Look at the Dirichlet Distribution: Robustness, Clustering, and Both Together

Salvatore D. Tomarchio (), Antonio Punzo, Johannes T. Ferreira and Andriette Bekker
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Salvatore D. Tomarchio: University of Catania
Antonio Punzo: University of Catania
Johannes T. Ferreira: University of Pretoria
Andriette Bekker: University of Pretoria

Journal of Classification, 2025, vol. 42, issue 1, No 3, 53 pages

Abstract: Abstract Compositional data have peculiar characteristics that pose significant challenges to traditional statistical methods and models. Within this framework, we use a convenient mode parametrized Dirichlet distribution across multiple fields of statistics. In particular, we propose finite mixtures of unimodal Dirichlet (UD) distributions for model-based clustering and classification. Then, we introduce the contaminated UD (CUD) distribution, a heavy-tailed generalization of the UD distribution that allows for a more flexible tail behavior in the presence of atypical observations. Thirdly, we propose finite mixtures of CUD distributions to jointly account for the presence of clusters and atypical points in the data. Parameter estimation is carried out by directly maximizing the maximum likelihood or by using an expectation-maximization (EM) algorithm. Two analyses are conducted on simulated data to illustrate the effects of atypical observations on parameter estimation and data classification, and how our proposals address both aspects. Furthermore, two real datasets are investigated and the results obtained via our models are discussed.

Keywords: Compositional data; Dirichlet distribution; Mode; Model-based clustering; Robustness (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00357-024-09480-4

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