Parallel MMF: a Multiresolution Approach to Matrix Computation

Abstract: Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for sparse matrices. We argue that this makes pMMF a valuable new computational primitive in its own right, and present experiments on using pMMF for two distinct purposes: compressing matrices and preconditioning large sparse linear systems.