Learning sparsity and structure of matrices with multiscale graph basis dictionaries

Many modern data analysis tasks often require one to efficiently handle and analyze large matrix-form datasets such as term-document matrices and spatiotemporal measurements made via sensor networks. Since such matrices are often shuffled and scrambled, they do not have spatial coherency and smoothness that usual images and photographs possess, and consequently, the conventional wavelets and their relatives cannot be used in practice. Instead we propose to use our multiscale basis dictionaries for graphs, i.e., the Generalized Haar-Walsh Transform. In particular, we build such dictionaries for columns and rows separately, extract the column best basis and the row best basis from the basis dictionaries, and construct the tensor product of such best bases, which turns out to reveal hidden dependency and underlying geometric structure in the given matrix data. Finally, we will demonstrate the effectiveness of our approach using the Science News database.