An improvement on LDA algorithm for face recognition

Linear discrimination analysis (LDA) technique is an important and well-developed area of image recognition and to date many linear discrimination methods have been put forward. Despite these efforts, there persist in the traditional LDA some weaknesses. In this paper, we propose a new LDA-based method that can overcome the drawback existed in the traditional LDA method. It redefines the between-class scatter by adding a weight function according to the between-class distance, which helps to separate the classes as much as possible. At the same time, in this method, we firstly remove the null space of total scatter matrix which has been proved to be the common null space of both between-class and within-class scatter matrix, and useless for discrimination. Then in the lower-dimensional projected space, the null space of the resulting within-class scatter matrix is calculated. This lower-dimensional null space, combined with the previous projection, represents a subspace of the whole null space of within-class scatter matrix, and is really useful for discrimination. The optimal discriminant vectors of LDA are derived from it. Experiment results show our method achieves better performance in comparison with the traditional LDA methods.