Unsupervised Deep Haar Scattering on Graphs

TL;DR

This paper introduces an unsupervised Haar scattering transform for graph-structured data, enabling invariant feature extraction and classification on high-dimensional signals with unknown graph geometry.

Contribution

It proposes a novel deep Haar scattering method on graphs that estimates multiscale neighborhoods and computes invariant descriptors without prior graph knowledge.

Findings

Effective classification on scrambled images.

Successful application to signals on irregular spherical grids.

Demonstrates robustness to unknown graph structures.

Abstract

The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of unknown graphs are estimated by minimizing an average total variation, with a pair matching algorithm of polynomial complexity. Supervised classification with dimension reduction is tested on data bases of scrambled images, and for signals sampled on unknown irregular grids on a sphere.