Robust Bilinear Probabilistic Principal Component Analysis

Abstract

Principal component analysis (PCA) is one of the most popular tools in multivariate exploratory data analysis. Its probabilistic version (PPCA) based on the maximum likelihood procedure provides a probabilistic manner to implement dimension reduction. Recently, the bilinear PPCA (BPPCA) model, which assumes that the noise terms follow matrix variate Gaussian distributions, has been introduced to directly deal with two-dimensional (2-D) data for preserving the matrix structure of 2-D data, such as images, and avoiding the curse of dimensionality. However, Gaussian distributions are not always available in real-life applications which may contain outliers within data sets. In order to make BPPCA robust for outliers, in this paper, we propose a robust BPPCA model under the assumption of matrix variate t distributions for the noise terms. The alternating expectation conditional maximization (AECM) algorithm is used to estimate the model parameters. Numerical examples on several synthetic and publicly available data sets are presented to demonstrate the superiority of our proposed model in feature extraction, classification and outlier detection.

Keywords

• 2-D data
• probabilistic principal component analysis
• AECM algorithm
• matrix variate Gaussian distributions
• matrix variate <i>t</i> distributions
• outliers