Gauss-Seidel based non-negative matrix factorization for gene expression clustering

Genome-wide expression data consists of millions of measurements towards large number of genes, and thus it is challenging for human beings to directly analyze such large-scale data. Clustering provides a more convenient way to analyze gene expression data because it can subdivide raw data into comprehensive classes. However, the number of probed genes is rather greater than the number of samples, and this makes conventional clustering methods perform unsatisfactorily. In this paper, we propose a Gauss-Seidel based non-negative matrix factorization (GSNMF) method to overcome such imbalance deficiency between features and samples. In particular, GSNMF it-eratively projects gene expression data onto the learned subspace followed by adaptively updating the cluster centroids based on the projected data. Since this data projection strategy significantly reduces the influence of imbalance between the number of samples and the number of genes, GSNMF performs better than traditional clustering methods in gene expression clustering. Since GSNMF updates each factor matrix by solution of a linear system obtained by the Gauss-Seidel method, it converges rapidly without neither complex line search nor matrix inverse operators. Experimental results on several cancer expression datasets confirm both efficiency and effectiveness of GSNMF comparing with the representative NMF methods and conventional clustering methods.