Wavelets on graphs via spectral graph theory
TLDR
A novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph using the spectral decomposition of the discrete graph Laplacian L, based on defining scaling using the graph analogue of the Fourier domain.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 2011-03-01 and is currently open access. It has received 1681 citations till now. The article focuses on the topics: Line graph & Spectral graph theory.read more
Citations
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Semi-Supervised Classification with Graph Convolutional Networks
Thomas Kipf,Max Welling +1 more
TL;DR: A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.
Posted Content
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
TL;DR: In this article, a spectral graph theory formulation of convolutional neural networks (CNNs) was proposed to learn local, stationary, and compositional features on graphs, and the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs while being universal to any graph structure.
Journal ArticleDOI
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
TL;DR: The field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process high-dimensional data on graphs as discussed by the authors, which are the analogs to the classical frequency domain and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs.
Proceedings Article
Convolutional neural networks on graphs with fast localized spectral filtering
TL;DR: This work presents a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs.
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Graph Neural Networks: A Review of Methods and Applications
Jie Zhou,Ganqu Cui,Shengding Hu,Zhengyan Zhang,Cheng Yang,Zhiyuan Liu,Lifeng Wang,Changcheng Li,Maosong Sun +8 more
TL;DR: A detailed review over existing graph neural network models is provided, systematically categorize the applications, and four open problems for future research are proposed.
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.
Book
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.