# Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics

arXiv: https://arxiv.org/abs/2406.00469 · HTML: https://mlsanity.com/paper/2406.00469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 76 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 22 of 22)

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- [Revisiting the Nystrom Method for Improved Large-Scale Machine Learning](https://mlsanity.com/paper/1303.1849/) (2013)
- [Learning Local Shape Descriptors from Part Correspondences With Multi-view Convolutional Networks](https://mlsanity.com/paper/1706.04496/) (2017)
- [Temporal Multiresolution Graph Neural Networks For Epidemic Prediction](https://mlsanity.com/paper/2205.14831/) (2022)
- [Multiresolution Kernel Approximation for Gaussian Process Regression](https://mlsanity.com/paper/1708.02183/) (2017)
- [Predicting COVID-19 pandemic by spatio-temporal graph neural networks: A New Zealand's study](https://mlsanity.com/paper/2305.07731/) (2023)
- [The Incremental Multiresolution Matrix Factorization Algorithm](https://mlsanity.com/paper/1705.05804/) (2017)

## Abstract (arXiv)

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