A Bayesian Fisher-EM algorithm for discriminative Gaussian subspace clustering
vendredi 23 avril 2021, 9h30 - 10h30
Gaussian subspace clustering models integrate clustering and dimension reduction, modeling data as a linear observations of a Gaussian mixture in a low-dimensional subspace. In this work, we introduce a Bayesian extension to the Fisher EM algorithm for high-dimensional data clustering, considering that the low dimensional subspace is discriminant in the sense of Fisher’s Linear Discriminant analysis. Modeling class dispersion with a Gaussian prior over the latent group means, inference relies on mixing a variational EM algorithm estimating the mixture parameters while the discriminative subspace is estimated separately, 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. We illustrate the algorithm performances over state-of-the-art Gaussian subspace clustering models on several high-dimensional and noisy scenarios, and discuss an application to single image denoising analogous to the HDMI algorithm of Houdard et.al. This work comes with a reference implementation for the R software in the FisherEM package available on CRAN.