Greedy clustering of count data through a mixture of multinomial PCA

TL;DR

This paper introduces a greedy clustering algorithm for count data using a mixture of multinomial PCA, combining variational inference with a branch & bound strategy, and demonstrates its effectiveness on medical report data.

Contribution

It presents a novel greedy clustering method based on mixture of multinomial PCA with joint inference and model selection criteria, improving clustering of count data.

Findings

Effective clustering of count data demonstrated on medical reports

Method shows robustness and improved performance in numerical experiments

Qualitative insights gained from real-world medical report application

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.