  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. Here 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.
