Greedy clustering of count data through a mixture of multinomial PCA

Nicolas Jouvin (), Pierre Latouche (), Charles Bouveyron (), Guillaume Bataillon () and Alain Livartowski ()
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Nicolas Jouvin: Université Paris 1 Panthéon Sorbonne, Laboratoire SAMM, EA 4543
Pierre Latouche: Université de Paris, MAP 5, UMR 8145
Charles Bouveyron: Université Côte d’Azur, Inria, CNRS, Laboratoire J.A. Dieudonné, Maasai Team
Guillaume Bataillon: Pôle de médecine diagnostique et théranostique, Institut Curie
Alain Livartowski: Institut Curie, Direction des Data

Computational Statistics, 2021, vol. 36, issue 1, No 1, 33 pages

Abstract: 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.

Keywords: Clustering; Mixture models; Count data; Dimension reduction; Topic modeling; Variational inference (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01008-9

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