Wednesday, September 17, 2014

Multiresolution Matrix Factorization

You probably recall the idea expressed in Sunday Morning Insight on Matrix Factorizations and the Grammar of Life, where one would iterate on several matrix factorization in order to provide a convinving decomposition of a data matrix. The idea is similar to diffusion wavelets and more recent  signal processing on graphs. Here is a new paper on the matter:  

Multiresolution Matrix Factorization by Risi Kondor, Nedelina Teneva and Vikas Garg

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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