Sparse robust matrix tri-factorization with application to cancer genomics

Nonnegative matrix tri-factorization (NMTF) X ≈ FSG^T with all matrices nonnegative can reveal simultaneous row and column clusters of X, as well as the associations among the two. In this work, a sparsity-promoting variant is proposed and a simple multiplicative algorithm is developed. The resulting sparse NMTF is further robustified to cope with presence of outliers in the data. A synthetic example illustrates the efficacy of the method. A novel application to cancer patient clustering and pathway analysis is presented using real datasets.