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Multiresolution Matrix Factorization
Authors: Risi Kondor, Nedelina Teneva and Vikas Garg
Conference: Proceedings of the 31st International Conference on Machine Learning (ICML-14)
Abstract: The types of large matrices that appear in modern Machine Learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecompositions. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nystrom approximations) and as a prior for matrix completion.
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