A Bayesian Fisher-EM algorithm for discriminative Gaussian subspace clustering

TL;DR

This paper introduces a Bayesian Fisher-EM algorithm for discriminative Gaussian subspace clustering, improving clustering accuracy in high-dimensional data through a variational EM approach and Bayesian modeling.

Contribution

It extends the discriminative latent mixture model to a Bayesian framework with a variational EM inference and Fisher-step for subspace estimation, including hyper-parameter estimation and model selection.

Findings

Superior performance over state-of-the-art models in simulations

Effective in high-dimensional noisy data scenarios

Successful application to single image denoising

Abstract

High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we extend it to the Bayesian framework. Modeling data as a mixture of Gaussians in a low-dimensional discriminative subspace, a Gaussian prior distribution is introduced over the latent group means and a family of twelve submodels are derived considering different covariance structures. Model inference is done with a variational EM algorithm, while the discriminative subspace is estimated via a Fisher-step maximizing an unsupervised Fisher criterion. An empirical Bayes procedure is proposed for the estimation of the prior hyper-parameters, and an integrated classification likelihood criterion is derived for selecting both the number of clusters and the submodel. The performances of the resulting Bayesian Fisher-EM algorithm are investigated in two thorough simulated scenarios, regarding both dimensionality as well as noise and assessing its superiority with respect to state-of-the-art Gaussian subspace clustering models. In addition to standard real data benchmarks, an application to single image denoising is proposed, displaying relevant results. This work comes with a reference implementation for the R software in the FisherEM package accompanying the paper.