
Graph Wavelet Neural Network
We present graph wavelet neural network (GWNN), a novel graph convolutio...
04/12/2019 ∙ by Bingbing Xu, et al. ∙ 64 ∙ shareread it

Neural networks and rational functions
Neural networks and rational functions efficiently approximate each othe...
06/11/2017 ∙ by Matus Telgarsky, et al. ∙ 0 ∙ shareread it

MotifNet: a motifbased Graph Convolutional Network for directed graphs
Deep learning on graphs and in particular, graph convolutional neural ne...
02/04/2018 ∙ by Federico Monti, et al. ∙ 0 ∙ shareread it

Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers
This paper presents a unified approach to the modeling and computation o...
07/02/2019 ∙ by Simon Etter, et al. ∙ 0 ∙ shareread it

On Spectral Graph Embedding: A NonBacktracking Perspective and Graph Approximation
Graph embedding has been proven to be efficient and effective in facilit...
01/01/2018 ∙ by Fei Jiang, et al. ∙ 0 ∙ shareread it

Spectral Filter Tracking
Visual object tracking is a challenging computer vision task with numero...
07/18/2017 ∙ by Zhen Cui, et al. ∙ 0 ∙ shareread it

Fourier Neural Networks: A Comparative Study
We review neural network architectures which were motivated by Fourier s...
02/08/2019 ∙ by Abylay Zhumekenov, et al. ∙ 0 ∙ shareread it
Rational Neural Networks for Approximating Jump Discontinuities of Graph Convolution Operator
For node level graph encoding, a recent important stateofart method is the graph convolutional networks (GCN), which nicely integrate local vertex features and graph topology in the spectral domain. However, current studies suffer from several drawbacks: (1) graph CNNs relies on Chebyshev polynomial approximation which results in oscillatory approximation at jump discontinuities; (2) Increasing the order of Chebyshev polynomial can reduce the oscillations issue, but also incurs unaffordable computational cost; (3) Chebyshev polynomials require degree Ω(poly(1/ϵ)) to approximate a jump signal such as x, while rational function only needs O(poly log(1/ϵ))liang2016deep,telgarsky2017neural. However, it's nontrivial to apply rational approximation without increasing computational complexity due to the denominator. In this paper, the superiority of rational approximation is exploited for graph signal recovering. RatioanlNet is proposed to integrate rational function and neural networks. We show that rational function of eigenvalues can be rewritten as a function of graph Laplacian, which can avoid multiplication by the eigenvector matrix. Focusing on the analysis of approximation on graph convolution operation, a graph signal regression task is formulated. Under graph signal regression task, its time complexity can be significantly reduced by graph Fourier transform. To overcome the local minimum problem of neural networks model, a relaxed Remez algorithm is utilized to initialize the weight parameters. Convergence rate of RatioanlNet and polynomial based methods on jump signal is analyzed for a theoretical guarantee. The extensive experimental results demonstrated that our approach could effectively characterize the jump discontinuities, outperforming competing methods by a substantial margin on both synthetic and realworld graphs.
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