Mixtures of robust probabilistic principal component analyzers

Mixtures of probabilistic principal component analyzers model high-dimensional nonlinear data by combining local linear models. Each mixture component is specifically designed to extract the local principal orientations in the data. An important issue with this generative model is its sensitivity to data lying off the low-dimensional manifold. In order to address this problem, the mixtures of robust probabilistic principal component analyzers are introduced. They take care of atypical points by means of a long tail distribution, the Student-t. It is shown that the resulting mixture model is an extension of the mixture of Gaussians, suitable for both robust clustering and dimensionality reduction. Finally, we briefly discuss how to construct a robust version of the closely related mixture of factor analyzers.