Model-based clustering of multivariate binary data with dimension reduction

TL;DR

This paper introduces a novel model-based clustering method for multivariate binary data that simultaneously identifies the optimal cluster structure and the low-dimensional subspace, enhancing interpretability and stability.

Contribution

It extends latent class analysis by incorporating dimension reduction with sparsity, and develops an EM algorithm for efficient optimization.

Findings

Effective in simulation studies

Successfully applied to real datasets

Provides interpretable low-dimensional representations

Abstract

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel procedure for simultaneously determining the optimal cluster structure for multivariate binary data and the subspace to represent that cluster structure. The method is based on a finite mixture model of multivariate Bernoulli distributions, and each component is assumed to have a low-dimensional representation of the cluster structure. This method can be considered an extension of the traditional latent class analysis model. Sparsity is introduced to the loading values, which produces the low-dimensional subspace, for enhanced interpretability and more stable extraction of the subspace. An EM-based algorithm is developed to efficiently solve the proposed optimization problem. We demonstrate the effectiveness of the proposed method by applying it to a simulation study and real datasets.