Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics
This work addresses the brittleness of existing MMF methods for modeling hierarchical graphs, offering a more robust approach for applications in graph learning, though it is incremental as it builds on prior MMF techniques.
The paper tackled the difficulty of finding Multiresolution Matrix Factorization (MMF) for graphs with complex structure by proposing a learnable version optimized with evolutionary metaheuristics and manifold optimization, resulting in a wavelet basis that far outperforms prior MMF algorithms and achieves competitive performance on tasks like molecular graph and node classification.
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 using metaheuristics, specifically evolutionary algorithms and directed evolution, along with Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and gives comparable performance on standard learning tasks on graphs. Furthermore, we construct the wavelet neural networks (WNNs) learning graphs on the spectral domain with the wavelet basis produced by our MMF learning algorithm. Our wavelet networks are competitive against other state-of-the-art methods in molecular graphs classification and node classification on citation graphs. We release our implementation at https://github.com/HySonLab/LearnMMF