Ye Yuan
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Some key Papers on Graph Spectral Theory and Graph Convolutional Networks

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Wavelets on Graphs via Spectral Graph Theory

Abstract

We propose a novel method for constructing wavelet transforms of functions de ned on the vertices of an arbitrary nite weighted graph. Our approach is based on de ning scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian . Given a wavelet generating kernel and a scale parameter , we define the scaled wavelet operator . The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. We explore the localization properties of the wavelets in the limit of ne scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing .

Introduction

Some data are defined on regular Euclidean spaces, such as time seriers data, image or videos. However, many interesting applications involve data defined on more topologically complicated domains.

Classical Wavelet Transform

Weighted Graphs and Spectral Graph Theory

Spectral Graph Wavelet Transform

Transform properties

Polynomial Approximation and Fast SGWT

Reconstruction

Implementation and examples

Conclusions and Future Work

Spectral Networks and Deep Locally Connected Networks on Graphs

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

References

[1] @inproceedings{defferrard2016convolutional, title={Convolutional neural networks on graphs with fast localized spectral filtering}, author={Defferrard, Micha{"e}l and Bresson, Xavier and Vandergheynst, Pierre}, booktitle={Advances in neural information processing systems}, pages={3844--3852}, year={2016} }

[2] @article{kipf2016semi, title={Semi-supervised classification with graph convolutional networks}, author={Kipf, Thomas N and Welling, Max}, journal={arXiv preprint arXiv:1609.02907}, year={2016} }

[3] @article{bruna2013spectral, title={Spectral networks and locally connected networks on graphs}, author={Bruna, Joan and Zaremba, Wojciech and Szlam, Arthur and LeCun, Yann}, journal={arXiv preprint arXiv:1312.6203}, year={2013} }

[4] @inproceedings{defferrard2016convolutional, title={Convolutional neural networks on graphs with fast localized spectral filtering}, author={Defferrard, Micha{"e}l and Bresson, Xavier and Vandergheynst, Pierre}, booktitle={Advances in neural information processing systems}, pages={3844--3852}, year={2016} }

[5] @article{hammond2011wavelets, title={Wavelets on graphs via spectral graph theory}, author={Hammond, David K and Vandergheynst, Pierre and Gribonval, R{'e}mi}, journal={Applied and Computational Harmonic Analysis}, volume={30}, number={2}, pages={129--150}, year={2011}, publisher={Elsevier} }