Multiprojection Local Discriminant Analysis

Abstract

Linear discriminant analysis (LDA) is a critical technology for dimensionality reduction (DR). However, LDA still suffers from the following issues. One is that the total number of features available from LDA is limited to the number of classes minus one, which severely limits its application, especially for the problems where the dimension of the features is much higher than the number of classes. Another one is that LDA only preserves the global information of the data while ignoring the local structure of the data, which degrades the performance. To overcome these disadvantages, a multiprojection local discriminant analysis (MLDA) of calculating the discriminant features is proposed in this paper. Specifically, we first make a simple but crucial transformation for the optimization problem of LDA, and then propose a novel multiprojection convex discriminant analysis framework that can extract an unlimited number of features and avoid the small sample size problem. In addition, an auto-optimized graph technology is cleverly integrated into the discriminant analysis framework to exploit the local structure of data. As a result, enough more discriminative and structured features can be extracted. Since two variables need to be optimized simultaneously in the proposed methods, an efficient iterative optimization algorithm is introduced to solve the proposed MLDA. Extensive experiments on several benchmark data sets have demonstrated the effectiveness of the proposed method.