Multiresolution Matrix Factorization
Risi Kondor, Nedelina Teneva, Vikas Garg · 2014
The types of large matrices that appear in mod-ern Machine Learning problems often have com-plex 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 intro-duces a new notion of matrix factorization that can capture structure in matrices at multiple dif-ferent scales. The resulting Multiresolution Ma-trix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nyström approximations) and as a prior for ma-trix completion. 1.