A class of Laplacian mutiwavelets bases for high-dimensional data

We introduce a framework for representing functions defined on high-dimensional data. In this framework, we propose to use the eigenvectors of the graph Laplacian to construct a multiresolution analysis on the data. This results in a one parameter family of orthogonal bases, which includes both Haar basis as well as the eigenvectors of the graph Laplacian. We describe a discrete fast transform for expansion in any of the bases in this family, and derive an asymptotic rate of coefficients decay. We demonstrate our construction using several numerical examples.

This is a joint work with Yoel Shkolnisky.