L_2,1 Norm regularized fisher criterion for optimal feature selection

Feature selection has been proved to be an effective way to improve the result of many pattern recognition tasks like image classification and automatic face recognition. Among all the methods, those based on Fisher criterion have received considerable attention owing to their efficiency and good generalization over classifiers. However, the original Fisher criterion-based methods ignore the inter-dependencies between different features. To this end, this paper proposes an optimized feature selection method which incorporates the l_2,1 norm regularization into the original Fisher criterion. The l_2,1 norm regularization term assures the sparsity of the feature selection matrix, which makes the feature selection result to be close to the globally optimized solution. Owing to the sparsity of the feature selection matrix, a normalization constraint constructed based on the inter-class scatter matrix of Fisher criterion is used to simplify the original problem, so that the solution of the feature selection problem can be derived from an iterative algorithm whose key step is to solve a generalized eigenvalue problem. Experiments on various data sets indicate that the proposed method provides higher accuracy in pattern recognition tasks compared with several existing approaches.