Deep Haar Scattering Networks

TL;DR

Deep Haar scattering networks use hierarchical, non-linear transforms to create permutation-invariant representations for classification, effectively handling graph-structured data with or without known connectivity.

Contribution

This paper introduces an orthogonal Haar scattering transform that models unsupervised deep learning and estimates graph connectivity through pair matching, enhancing classification on structured data.

Findings

Effective classification on image and graph data.

Unsupervised pair matching estimates graph connectivity.

Permutation-invariant representations improve robustness.

Abstract

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.