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Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrixfactorization algorithms in that it does not make a low rank assumption. Thismakes MMF especially well suited to modeling certain types of graphs withcomplex multiscale or hierarchical strucutre. While MMF promises to yields auseful wavelet basis, finding the factorization itself is hard, and existinggreedy methods tend to be brittle. In this paper we propose a learnable versionof MMF that carfully optimizes the factorization with a combination ofreinforcement learning and Stiefel manifold optimization throughbackpropagating errors. We show that the resulting wavelet basis faroutperforms prior MMF algorithms and provides the first version of this type offactorization that can be robustly deployed on standard learning tasks.

Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs