Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs

TL;DR

This paper introduces a learnable multiresolution matrix factorization method optimized via reinforcement learning and manifold techniques, enabling robust wavelet basis construction for complex graph structures.

Contribution

It presents a novel learnable MMF approach that enhances robustness and performance over prior greedy algorithms for graph wavelet basis construction.

Findings

Wavelet basis significantly outperforms previous MMF algorithms.

The method is robustly deployable on standard learning tasks.

Learned MMF achieves better modeling of complex multiscale graph structures.

Abstract

Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yields a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper we propose a learnable version of MMF that carfully optimizes the factorization with a combination of reinforcement learning and Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and provides the first version of this type of factorization that can be robustly deployed on standard learning tasks.