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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
Face Recognition System Based on Spectral Graph Wavelet Theory
TL;DR: The results indicate that the proposed system based on SGWT is better than wavelet transform and 94% recognition accuracy is achieved.
Proceedings ArticleDOI
Sparse inverse bilateral filters for image processing
TL;DR: In this paper, a sparse graph is proposed to approximate the inverse covariance matrix of a dense bilateral filter kernel matrix, which is analogous to the idea of finding a sparse covariance of a Gaussian Markov random field (GMRF) with a dense covariance matrices, which allows for low frequency representation of the image similar to the bilateral filter eigenvectors.
Book ChapterDOI
Classification of Relationship in Argumentation Using Graph Convolutional Network
Dimmy Magalhães,Aurora Pozo +1 more
TL;DR: This study proposes ArgGCN, a framework based in GCN method applied to the classification of relationships between arguments, and achieves promising results on the UKP Aspect, AFS, and Microtext corpus.
Proceedings ArticleDOI
Construction of undersampled graph filter banks via row subset selection
Akie Sakiyama,Yuichi Tanaka +1 more
TL;DR: A construction method of M-channel under-sampled spectral graph filter banks that can be applied to any kind of undirected graphs, use arbitrary critically sampled or oversampled analysis filters, and obtain low redundancy, which is less than 1, regardless of the number of the analysis filters.
Dissertation
Numerische Methoden zur Analyse hochdimensionaler Daten
TL;DR: A new denosing method for high-dimensional data, a wavelet shrinkage method for smoothing of noisy sample values of an underlying multivariate piecewise continuous function, where the sample points may be scattered.
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.