Risi Kondor University of Chicago risi@uchicago.edu 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.