Greedy clustering of count data through a mixture of multinomial PCA

DOI10.48550/ARXIV.1909.00721zbMATH Open1505.62208arXiv1909.00721OpenAlexW3101282283MaRDI QIDQ131099

Alain Livartowski, Guillaume Bataillon, Guillaume Bataillon, Nicolas Jouvin, Pierre Latouche, Charles Bouveyron, Alain Livartowski, Pierre Latouche, Charles Bouveyron, Nicolas Jouvin

Publication date: 2 September 2019

Published in: Computational Statistics (Search for Journal in Brave)

Abstract: Count data is becoming more and more ubiquitous in a wide range of applications, with datasets growing both in size and in dimension. In this context, an increasing amount of work is dedicated to the construction of statistical models directly accounting for the discrete nature of the data. Moreover, it has been shown that integrating dimension reduction to clustering can drastically improve performance and stability. In this paper, we rely on the mixture of multinomial PCA, a mixture model for the clustering of count data, also known as the probabilistic clustering-projection model in the literature. Related to the latent Dirichlet allocation model, it offers the flexibility of topic modeling while being able to assign each observation to a unique cluster. We introduce a greedy clustering algorithm, where inference and clustering are jointly done by mixing a classification variational expectation maximization algorithm, with a branch & bound like strategy on a variational lower bound. An integrated classification likelihood criterion is derived for model selection, and a thorough study with numerical experiments is proposed to assess both the performance and robustness of the method. Finally, we illustrate the qualitative interest of the latter in a real-world application, for the clustering of anatomopathological medical reports, in partnership with expert practitioners from the Institut Curie hospital.

Full work available at URL: https://arxiv.org/abs/1909.00721

zbMATH Keywords

clusteringdimension reductioncount datamixture modelsvariational inferencetopic modeling

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Factor analysis and principal components; correspondence analysis (62H25) Classification and discrimination; cluster analysis (statistical aspects) (62H30)

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