The large similarity matrices that appear in simulations of multi-body systems often exhibit complex hierarchical structure, which goes beyond what can be uncovered by traditional linear algebra tools, such as eigendecomposition. In this talk I describe a new notion of matrix factorization inspired by multiresolution analysis 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 and as a prior for matrix completion. The work presented in this talk is joint with Nedelina Teneva and Vikas Garg.
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