The estimation of dimensionality in gene expression data using Nonnegative Matrix Factorization

Nonnegative matrix factorization and other decomposition methods have proven to offer significant advantages for the interpretation of genome-wide gene expression data. However, unlike analytic methods, they suffer from instability in the inferred factors or patterns as the dimensionality is changed. We present here two statistics, one mathematical and one biological, that estimate the dimensionality. We show that they provide close though not identical estimates, and that they provide strong evidence for elimination of some potential factorizations.