Deep Unfolding for Non-Negative Matrix Factorization with Application to Mutational Signature Analysis

Non-negative matrix factorization (NMF) is a fundamental matrix decomposition technique that is used primarily for dimensionality reduction and is increasing in popularity in the biological domain. Although finding a unique NMF is generally not possible, there are various iterative algorithms for NMF optimization that converge to locally optimal solutions. Such techniques can also serve as a starting point for deep learning methods that unroll the algorithmic iterations into layers of a deep network. In this study, we develop unfolded deep networks for NMF and several regularized variants in both a supervised and an unsupervised setting. We apply our method to various mutation data sets to reconstruct their underlying mutational signatures and their exposures. We demonstrate the increased accuracy of our approach over standard formulations in analyzing simulated and real mutation data.