Locality-Preserving Multiprojection Discriminant Analysis

Linear discriminant analysis (LDA), as an effective feature extraction method, has been widely applied in high-dimensional data analysis. However, its discriminative performance is still severely limited by the following factors. First, the restriction on the total number of features available from LDA has seriously limited its application to problems where the feature dimension is much larger than the number of classes. Second, LDA cannot deal with data containing multiple clusters (or subclasses) within a class because it cannot correctly depict the local structure of the data. To alleviate this issue, we propose a locality-preserving multiprojection discriminant analysis (LPMDA) model to extract more discriminative features preserving local structure. Specifically, LPMDA rephrases the objective function of LDA as a convex discriminant analysis framework from the perspective of metric learning, allowing for extracting more features than the number of classes. Furthermore, an auto-optimized graph technique is also integrated into the discriminant analysis framework to explore the local structure of the data. An efficient iterative optimization algorithm is presented to solve LPMDA. Extensive experiments on several benchmark datasets confirm the effectiveness of the proposed method.