Variable selection for mixed data clustering: a model-based approach

TL;DR

This paper introduces two novel model-based variable selection methods for mixed data clustering using latent class analysis, improving efficiency and avoiding computationally intensive procedures.

Contribution

It presents two approaches based on BIC and MICL for variable selection in mixed data clustering, avoiding traditional suboptimal and costly algorithms.

Findings

Both methods perform well on simulated data.

They are effective on real-world datasets.

The approaches handle missing data efficiently.

Abstract

We propose two approaches for selecting variables in latent class analysis (i.e.,mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in optimizing the BIC with a modified version of the EM algorithm. This approach simultaneously performs both model selection and parameter inference. The second approach consists in maximizing the MICL, which considers the clustering task, with an algorithm of alternate optimization. This approach performs model selection without requiring the maximum likelihood estimates for model comparison, then parameter inference is done for the unique selected model. Thus, the benefits of both approaches is to avoid the computation of the maximum likelihood estimates for each model comparison. Moreover, they also avoid the use of the standard algorithms for variable selection which are often suboptimal (e.g. stepwise method) and computationally expensive. The case of data with missing values is also discussed. The interest of both proposed criteria is shown on simulated and real data.