Unsupervised Deep Haar Scattering on Graphs

By Xu Chen, Xiuyuan Cheng, Stéphane Mallat. 2014

55 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Graph Learning

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Citations in the corpus

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, background): “atestodeﬁneconvolutionoperations 3 onmeshpatches,andformulatedadeeplearningarchitecturewhichallowscomparisonacrossdiﬀerent manifolds. Theyobtainedstate-of-the-artresultsfor3Dshaperecognitiontasks. In [6] and [30], the authors investigated the construction of Haar wavelet transforms on graphs usingad”
Deep Convolutional Networks on Graph-Structured Data (2015, methodology): “Also, [3] considers the problem of learning a deep architecture through a series of Haar contractions, which are learnt using an unsupervised pairing criteria over the features.”