Abstract

Fisher’s linear discriminant analysis (LDA), one of the most popular dimensionality reduction algorithms for classification, has three particular problems: it fails to find the nonlinear structure hidden in the high dimensional data; it assumes all samples contribute equivalently to reduce dimension for classification; and it suffers from the matrix sin- gularity problem. In this paper, we propose a new algorithm, termed Discriminative Locality Alignment (DLA), to deal with these problems. The algorithm operates in the following three stages: first, in part op- timization, discriminative information is imposed over patches, each of which is associated with one sample and its neighbors; then, in sample weighting, each part optimization is weighted by the margin degree, a measure of the importance of a given sample; and finally, in whole align- ment, the alignment trick is used to align all weighted part optimiza- tions to the whole optimization. Furthermore, DLA is extended to the semi-supervised case, i.e., semi-supervised DLA (SDLA), which utilizes unlabeled samples to improve the classification performance. Thorough empirical studies on the face recognition demonstrate the effectiveness of both DLA and SDLA.