Robust Bayesian PCA with Student#x2019;s t-distribution: The variational inference approach

摘要

Principal component analysis (PCA) is a well established approach for computing the principal subspace of large image sets. It is widely used in low-level computer vision tasks (e.g., face recognition, subspace based visual tracking). One of the central issues in the use of PCA for image modelling is that it is very sensitive to outliers since its formulation is based on Gaussian density model. Lately, more heavy-tailed distribution (i.e., Student’s t-distribution) is introduced to increase the robustness of traditional PCA. But the robust version of PCA is expressed as the maximum likelihood solution of a probabilistic latent variable model. This reformulation raises the question of how to determine the optimal number of principal components to be retained. In this paper, we develop a Bayesian model selection approach to estimate the true dimensionality of the data. The proposed algorithm is based on a new Bayesian treatment of robust Student’s t-distribution PCA. A variational approximation scheme is used to infer key parameters in the model. We illustrate how this leads to simultaneous optimal dimensionality selection and accurate principal components recovery.