Sparse maximum margin discriminant analysis for feature extraction and gene selection on gene expression data

Dimensionality reduction is necessary for gene expression data classification. In this paper, we propose a new method for reducing the dimensionality of gene expression data. First, based on a sparse representation, we developed a new criterion for characterizing the margin, which is called sparse maximum margin discriminant analysis (SMMDA); this approach can be used to find an optimal transform matrix such that the sparse margin is maximal in the transformed space. Second, using SMMDA, we present a new feature extraction method for gene expression data. Third, based on SMMDA, we propose a new discriminant gene selection method. During gene selection, we first found the one-dimensional projection of the gene expression data in the most separable direction using SMMDA. Then, we applied the sparse representation technique to regress the projection, and we obtained the relevance vector for the gene set. Discriminant genes were then selected according to this vector. Compared with the conventional method of maximum margin discriminant analysis, the proposed SMMDA method successfully avoids the difficulty of parameter selection. Extensive experiments using publicly available gene expression datasets showed that SMMDA is efficient for feature extraction and gene selection.