An automated approach for determining the number of components in non-negative matrix factorization with application to mutational signature learning

Non-negative matrix factorization (NMF) is a popular method for finding a low rank approximation of a matrix, thereby revealing the latent components behind it. In genomics, NMF is widely used to interpret mutation data and derive the underlying mutational processes and their activities. A key challenge in the use of NMF is determining the number of components, or rank of the factorization. Here we propose a novel method, CV2K, to choose this number automatically from data that is based on a detailed cross validation procedure combined with a parsimony consideration. We apply our method for mutational signature analysis and demonstrate its utility on both simulated and real data sets. In comparison to previous approaches, some of which involve human assessment, CV2K leads to improved predictions across a wide range of data sets.