Abstract
Nonnegative Matrix Factorization (NMF) has proved to be an effective method for unsupervised clustering analysis of gene expression data. By the nonnegativity constraint, NMF provides a decomposition of the data matrix into two matrices that have been used for clustering analysis. However, the decomposition is not unique. This allows different clustering results to be obtained, resulting in different interpretations of the decomposition. To alleviate this problem, some existing methods directly enforce uniqueness to some extent by adding regularization terms in the NMF objective function. Alternatively, various normalization methods have been applied to the factor matrices; however, the effects of the choice of normalization have not been carefully investigated. Here we investigate the performance of NMF for the task of cancer class discovery, under a wide range of normalization choices. After extensive evaluations, we observe that the maximum norm showed the best performance, although the maximum norm has not previously been used for NMF. Matlab codes are freely available from: http://maths.nuigalway.ie/~haixuanyang/pNMF/pNMF.htm.