Unsupervised Deep Haar Scattering on Graphs
This addresses the challenge of graph-based classification when graph structure is unknown, offering a method for domains like image processing and signal analysis, though it appears incremental as it builds on existing wavelet and scattering transform concepts.
The paper tackles the problem of classifying high-dimensional data on graphs with unknown geometry by introducing an unsupervised Haar scattering transform that computes invariant signal descriptors, achieving competitive classification results on scrambled images and signals on unknown irregular spherical grids.
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.