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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.

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Citations
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Proceedings ArticleDOI

Disentangling and Unifying Graph Convolutions for Skeleton-Based Action Recognition

TL;DR: A simple method to disentangle multi-scale graph convolutions and a unified spatial-temporal graph convolutional operator named G3D are presented and a powerful feature extractor named MS-G3D is developed based on which the model outperforms previous state-of-the-art methods on three large-scale datasets.
Posted Content

Graph Neural Networks in Recommender Systems: A Survey

TL;DR: This article provides a taxonomy of GNN-based recommendation models according to the types of information used and recommendation tasks and systematically analyze the challenges of applying GNN on different types of data.
Proceedings ArticleDOI

MGAE: Marginalized Graph Autoencoder for Graph Clustering

TL;DR: A marginalized graph convolutional network is proposed to corrupt network node content, allowing node content to interact with network features, and marginalizes the corrupted features in a graph autoencoder context to learn graph feature representations.
Proceedings ArticleDOI

Dual Graph Convolutional Networks for Graph-Based Semi-Supervised Classification

TL;DR: This paper presents a simple and scalable semi-supervised learning method for graph-structured data in which only a very small portion of the training data are labeled, and introduces an unsupervised temporal loss function for the ensemble.
Proceedings ArticleDOI

Robust Graph Convolutional Networks Against Adversarial Attacks

TL;DR: Robust GCN (RGCN), a novel model that "fortifies'' GCNs against adversarial attacks by adopting Gaussian distributions as the hidden representations of nodes in each convolutional layer, which can automatically absorb the effects of adversarial changes in the variances of the Gaussian distribution.
References
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Book

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.
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Functional analysis

Walter Rudin
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.
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