Open AccessPosted Content
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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Graph convolutional neural networks for the travelling salesman problem
TL;DR: This paper introduces a novel deep learning approach for approximately solving the most famous NP-hard problem in recent history, the Travelling Salesman Problem and focuses on the 2D Euclidean TSP and uses Graph Convolutional Neural Networks and beam search to predict a valid TSP tour given an input graph with up to 100 nodes.
Proceedings ArticleDOI
A Novel Dynamic Mesh Sequence Compression Framework for Progressive Streaming
TL;DR: Experimental results show that the proposed method can realize progressive streaming of mesh sequence and outperforms state-of-the-art methods in terms of storage space requirement and minimizing the reconstruction error.
Posted Content
Graph Generation via Scattering
Dongmian Zou,Gilad Lerman +1 more
TL;DR: A graph generation model that uses a recent adaptation of Mallat's scattering transform to graphs, naturally composed of an encoder and a decoder that is adapted to specific tasks, such as link prediction, signal generation on graphs and full graph and signal generation.
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Every Node Counts: Self-Ensembling Graph Convolutional Networks for Semi-Supervised Learning
TL;DR: Self-Ensembling GCN (SEGCN) as mentioned in this paper is a semi-supervised graph convolutional network with a student model and a teacher model, where the student model not only learns to correctly classify the labeled nodes, but also tries to be consistent with the teacher on unlabeled nodes in more challenging situations, such as a high dropout rate and graph collapse.
Journal ArticleDOI
Multi-windowed vertex-frequency analysis for signals on undirected graphs
TL;DR: Experimental results show that the proposed two types of frames can efficiently extract vertex-frequency features of synthetic graph signals and anomaly data can also be detected by these frames.
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.
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.