Abstract
Face recognition is one of the most fundamental functions for surveillance, information retrieval, robot vision, and so on. Among many methods proposed for face recognition, linear approaches such as principal component analysis (PCA) and linear discriminant analysis (LDA) have attracted great attention because of their simplicity. Generally speaking, LDA outperforms PCA because LDA may preserve the discriminative information better than PCA. However, when the number of training examples is small, LDA cannot be used directly because the within-class scatter matrix Sw might be singular. This is known as the small sample size (SSS) problem. To solve this problem, we can use PCA first to reduce the dimensionality of the feature space, and then adopt LDA. Another approach to solve the SSS problem is the null space (NS) approach. In this approach, only information contained in the null space of Sw is used for recognition. In our study, however, we found through experiments that some important discriminative information is also contained in the range space of Sw. Based on this observation, we propose a rough null space (RNS) approach. Experimental results on three public face databases show that the RNS approach is more effective than PCA, LDA and NS.
