Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs
This work addresses the brittleness of existing MMF methods for graph modeling, offering a more reliable tool for researchers and practitioners in machine learning and graph analysis.
The paper tackled the challenge of learning Multiresolution Matrix Factorization (MMF) for graphs with complex structures by proposing a learnable version that optimizes the factorization using reinforcement learning and Stiefel manifold optimization, resulting in a wavelet basis that significantly outperforms prior MMF algorithms and enables robust deployment on standard learning tasks.
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.