Non-parametric Multi-Partitions Clustering

TL;DR

This paper introduces a non-parametric multi-partitions clustering method that identifies variable blocks and their mixture components without parametric assumptions, using discretization and penalized likelihood for model selection.

Contribution

It extends multi-partitions clustering to a non-parametric setting by discretizing data and applying penalized likelihood, ensuring consistency and efficiency.

Findings

Method performs well on simulated data.

Consistency of the clustering procedure is proven.

Efficient optimization algorithm is proposed.

Abstract

In the framework of model-based clustering, a model, called multi-partitions clustering, allowing several latent class variables has been proposed. This model assumes that the distribution of the observed data can be factorized into several independent blocks of variables, each block following its own mixture model. In this paper, we assume that each block follows a non parametric latent class model, {\it i.e.} independence of the variables in each component of the mixture with no parametric assumption on their class conditional distribution. The purpose is to deduce, from the observation of a sample, the number of blocks, the partition of the variables into the blocks and the number of components in each block, which characterise the proposed model. By following recent literature on model and variable selection in non-parametric mixture models, we propose to discretize the data into bins. This permits to apply the classical multi-partition clustering procedure for parametric multinomials, which are based on a penalized likelihood method (\emph{e.g.} BIC). The consistency of the procedure is obtained and an efficient optimization is proposed. The performances of the model are investigated on simulated data.