Structurally-constrained gradient descent for matrix factorization in haplotype assembly problems

Abstract

In matrix decomposition problems, one often seeks to represent a data matrix by the product of two matrices — one capturing meaningful information contained in the data and the other specifying how this information is combined to generate the data matrix. We consider matrix decomposition that arises in haplotype assembly, an important problem in genomics. The observed matrix contains noisy samples of the product of an informative matrix with rows having entries from a finite alphabet and a matrix with rows that are standard unit basis. Structurally-constrained gradient descent algorithm for finding the two aforementioned matrices is proposed and its convergence is analyzed. Simulation results demonstrate superior accuracy and speed of the proposed method compared to state-of-the-art haplotype assembly techniques.