Fast Nonnegative Matrix Factorization andApplications to Pattern Extraction, Deconvolutionand Imputation

Abstract

Nonnegative matrix factorization (NMF) is a technique widely used in various fields, including artificial intelligence (AI), signal processing and bioinformatics. However existing algorithms and R packages cannot be applied to large matrices due to their slow convergence, and cannot handle missing values. In addition, most NMF research focuses only on blind decompositions: decomposition without utilizing prior knowledge. We adapt the idea of sequential coordinate-wise descent to NMF to increase the convergence rate. Our NMF algorithm thus handles missing values naturally and integrates prior knowledge to guide NMF towards a more meaningful decomposition. To support its use, we describe a novel imputation-based method to determine the rank of decomposition. All our algorithms are implemented in the R package NNLM, which is freely available on CRAN.