Whitened LDA for face recognition

Over the years, many Linear Discriminant Analysis (LDA) algorithms have been proposed for the study of high dimensional data in a large variety of problems. An intrinsic limitation of classical LDA is the so-called "small sample size (3S) problem" that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the 3S problems. However none of the previous methods could solve the 3S problem completely in the sense that it can keep all the discriminative features with a low computational cost. By applying LDA after whitening data, we proposed the Whitened LDA (WLDA) which can find the most discriminant features without facing the 3S problem. In WLDA, only eigenvalue problems instead of generalized eigenvalue problems are performed, leading to the low computation cost of WLDA. Experimental results are shown using two most popular Yale and ORL databases. Comparisons are given against Linear Discriminant Analysis (LDA), Direct LDA (DLDA), Null space LDA (NLDA) and several matrix-based subspace analysis approaches developed recently. We show that our method is always the best.