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Wavelets on Graphs via Spectral Graph Theory
TLDR
In this paper, the spectral graph wavelet operator is defined based on spectral decomposition of the discrete graph Laplacian, and a wavelet generating kernel and a scale parameter are used to localize this operator to an indicator function.Abstract:
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled wavelet operator $T_g^t = g(t\L)$. The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on $g$, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing $\L$. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.read more
Citations
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Journal ArticleDOI
Multi-Level Downsampling of Graph Signals via Improved Maximum Spanning Trees
Xianwei Zheng,Xianwei Zheng,Xianwei Zheng,Yuan Yan Tang,Jiantao Zhou,Jianjia Pan,Shouzhi Yang,Youfa Li,Patrick S. P. Wang +8 more
TL;DR: A novel and efficient method to detect and reduce the downsampling unbalance generated by the MST-based method is proposed and results on synthetic and real-world social network data show that downsamplings unbalance can be efficiently detected and then reduced by this method.
Journal ArticleDOI
Exploiting structural similarity in network reliability analysis using graph learning
TL;DR: It is concluded that the proposed structural similarity, component clustering, and graph learning approach are effective in simplifying the complexity of the network systems and reducing the computational cost for complex network analysis.
Patent
Graph convolution based gene prioritization on heterogeneous networks
Thomas Joseph,Aditya Rao,Naveen Sivadasan,Saipradeep Govindakrishnan Vangala,Sujatha Kotte,Rajgopal Srinivasan +5 more
TL;DR: In this article, a graph convolution-based gene prioritization method for heterogeneous networks is proposed, which includes obtaining a set of entities for human rare diseases from one or more sources containing rare diseases, genes, phenotypes for rare diseases and biological pathways.
Proceedings ArticleDOI
Community mining with graph filters for correlation matrices
TL;DR: An algorithm to detect multiscale communities, by filtering global modes and random parts using properties that are specific to the distribution of correlation eigenvalues, which yields a weighted hierarchy of communities.
Proceedings ArticleDOI
Spatio-Temporal Graph Convolutional Networks for Short-Term Traffic Forecasting
TL;DR: The considered graph convolutional networks are able to efficiently capture spatio-temporal correlations in traffic data and outperforms the baseline methods on the transportation network of the Samara city, Russia.
References
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A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Proceedings ArticleDOI
Object recognition from local scale-invariant features
TL;DR: Experimental results show that robust object recognition can be achieved in cluttered partially occluded images with a computation time of under 2 seconds.
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Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.