Weighted and robust learning of subspace representations

A reliable system for visual learning and recognition should enable a selective treatment of individual parts of input data and should successfully deal with noise and occlusions. These requirements are not satisfactorily met when visual learning is approached by appearance-based modeling of objects and scenes using the traditional PCA approach. In this paper we extend standard PCA approach to overcome these shortcomings. We first present a weighted version of PCA, which, unlike the standard approach, considers individual pixels and images selectively, depending on the corresponding weights. Then we propose a robust PCA method for obtaining a consistent subspace representation in the presence of outlying pixels in the training images. The method is based on the EM algorithm for estimation of principal subspaces in the presence of missing data. We demonstrate the efficiency of the proposed methods in a number of experiments.