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.

**Join the CompressiveSensing subreddit or the Google+ Community and post there !**

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

## No comments:

Post a Comment