Probabilistic principal component analysis (PPCA), as a special linear latent variable model, is a popular probabilistic dimension reduction model for 1D data. Unfortunately, PPCA incurs the so-called curse of dimensionality when applied to 2D data such as images. To overcome this problem, in this paper a novel probabilistic model called bilinear PPCA (BPPCA) to perform dimension reduction for 2D data is proposed. Practical and efficient model estimation algorithm are developed. Unlike existing model PSOPCA that follows from minimum-error formulation of PCA, BPPCA is motivated by maximum-variance formulation of PCA. For 2D data, these two different formulations lead to different model behaviors. The necessity of BPPCA is testified with a practical application in face recognition. Importantly, BPPCA signals a breakthrough from traditional linear latent variable models to the bilinear ones.
Keywords: PCA; PPCA; Two-dimensional data; Image analysis
Biography: Dr. Philip Yu is an Associate Professor of the University of Hong Kong. His main research interests include computational statistics, ranking methods, and financial data mining and risk management. He has published more than 55 papers in international referred journals. He is currently Vice President of Hong Kong Statistical Society.