Clustering gene expression data using probabilistic non-negative matrix factorization

Non-negative matrix factorization (NMF) has proven to be a useful decomposition for multivariate data. Specifically, NMF appears to have advantages over other clustering methods, such as hierarchical clustering, for identification of distinct molecular patterns in gene expression profiles. The NMF algorithm, however, is deterministic. In particular, it does not take into account the noisy nature of the measured genomic signals. In this paper, we extend the NMF algorithm to the probabilistic case, where the data is viewed as a stochastic process. We show that the probabilistic NMF can be viewed as a weighted regularized matrix factorization problem, and derive the corresponding update rules. Our simulation results show that the probabilistic non-negative matrix factorization (PNMF) algorithm is more accurate and more robust than its deterministic homologue in clustering cancer subtypes in a leukemia microarray dataset.