  Multiresolution Matrix Factorization (MMF) was recently introduced as an
alternative to the dominant low-rank paradigm in order to capture structure in
matrices at multiple different scales. Using ideas from multiresolution
analysis (MRA), MMF teased out hierarchical structure in symmetric matrices by
constructing a sequence of wavelet bases. While effective for such matrices,
there is plenty of data that is more naturally represented as nonsymmetric
matrices (e.g. directed graphs), but nevertheless has similar hierarchical
structure. In this paper, we explore techniques for extending MMF to any square
matrix. We validate our approach on numerous matrix compression tasks,
demonstrating its efficacy compared to low-rank methods. Moreover, we also show
that a combined low-rank and MMF approach, which amounts to removing a small
global-scale component of the matrix and then extracting hierarchical structure
from the residual, is even more effective than each of the two complementary
methods for matrix compression.
