We propose a new methodology for two-way cluster analysis of gene expression data using a novel sparse matrix factorization technique that produces a decomposition of a matrix in a set of sparse factors. This method produces a set of bases and coding matrices that are not only able to represent the original data, but they also extract important localized parts-based patterns. We applied the method to gene expression data sets in an attempt to uncover latent relationships between samples and genes in DNA microarray experiments.