An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning. It implements non-linear contractions, which are optimized for classification, with an unsupervised pair matching algorithm, of polynomial complexity. A structured Haar scattering over graph data computes permutation invariant representations of groups of connected points in the graph. If the graph connectivity is unknown, unsupervised Haar pair learning can provide a consistent estimation of connected dyadic groups of points. Classification results are given on image data bases, defined on regular grids or graphs, with a connectivity which may be known or unknown.
@article{arxiv.1509.09187,
title = {Deep Haar Scattering Networks},
author = {Xiuyuan Cheng and Xu Chen and Stephane Mallat},
journal= {arXiv preprint arXiv:1509.09187},
year = {2015}
}