Regularized singular value decomposition: a sparse dimension reduction technique

Singular value decomposition (SVD) is a useful multivariate technique for dimension reduction. It has been successfully applied to analyze microarray data, where the eigen vectors are called eigen-genes/arrays. One weakness associated with the SVD is the interpretation. The eigen-genes are essentially linear combinations of all the genes. It is desirable to have sparse SVD, which retains the dimension reduction property but also the eigen vectors are linear combinations of only a small subset of genes. In this paper we formally propose a statistical framework for sparse SVD, which is a generalization of traditional SVD. Our formulation of sparse SVD also bears the close connection to the penalized t-/F-statistics for differential gene expression detection, which can be viewed as the supervised sparse dimension reduction technique.