Relevant bibliographies by topics / Graph wavelets

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Graph wavelets'

Author: Grafiati
Published: 18 May 2024

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Journal articles on the topic "Graph wavelets"

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Wu, Jiasong, Fuzhi Wu, Qihan Yang, Yan Zhang, Xilin Liu, Youyong Kong, Lotfi Senhadji, and Huazhong Shu. "Fractional Spectral Graph Wavelets and Their Applications." Mathematical Problems in Engineering 2020 (November 6, 2020): 1–18. http://dx.doi.org/10.1155/2020/2568179.

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One of the key challenges in the area of signal processing on graphs is to design transforms and dictionary methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier transform (GFT) to spectral graph fractional Fourier transform (SGFRFT), which is then used to define a novel transform named spectral graph fractional wavelet transform (SGFRWT), which is a generalized and extended version of spectral graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and implemented based on Fourier series approximation. Some potential applications of SGFRWT are also presented.
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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (March 2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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Bastos, Anson, Abhishek Nadgeri, Kuldeep Singh, Toyotaro Suzumura, and Manish Singh. "Learnable Spectral Wavelets on Dynamic Graphs to Capture Global Interactions." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 6779–87. http://dx.doi.org/10.1609/aaai.v37i6.25831.

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Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation, which essentially only captures the low pass signals and local interactions. In this work, we go beyond current approaches to incorporate global features for effectively learning representations of a dynamically evolving graph. We propose to do so by capturing the spectrum of the dynamic graph. Since static methods to learn the graph spectrum would not consider the history of the evolution of the spectrum as the graph evolves with time, we propose an approach to learn the graph wavelets to capture this evolving spectra. Further, we propose a framework that integrates the dynamically captured spectra in the form of these learnable wavelets into spatial features for incorporating local and global interactions. Experiments on eight standard datasets show that our method significantly outperforms related methods on various tasks for dynamic graphs.
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Paul, Okuwobi Idowu, and Yong Hua Lu. "Facial Prediction and Recognition Using Wavelets Transform Algorithm and Technique." Applied Mechanics and Materials 666 (October 2014): 251–55. http://dx.doi.org/10.4028/www.scientific.net/amm.666.251.

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An efficient facial representation is a crucial step for successful and effective performance of cognitive tasks such as object recognition, fixation, facial recognition system, etc. This paper demonstrates the use of Gabor wavelets transform for efficient facial representation and recognition. Facial recognition is influenced by several factors such as shape, reflectance, pose, occlusion and illumination which make it even more difficult. Gabor wavelet transform is used for facial features vector construction due to its powerful representation of the behavior of receptive fields in human visual system (HVS). The method is based on selecting peaks (high-energized points) of the Gabor wavelet responses as feature points. This paper work introduces the use of Gabor wavelets transform for efficient facial representation and recognition. Compare to predefined graph nodes of elastic graph matching, the approach used in this paper has better representative capability for Gabor wavelets transform. The feature points are automatically extracted using the local characteristics of each individual face in order to decrease the effect of occluded features. Based on the experiment, the proposed method performs better compared to the graph matching and eigenface based methods. The feature points are automatically extracted using the local characteristics of each individual face in order to decrease the effect of occluded features. The proposed system is validated using four different face databases of ORL, FERRET, Purdue and Stirling database.
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Xu, Mingxing, Wenrui Dai, Chenglin Li, Junni Zou, Hongkai Xiong, and Pascal Frossard. "Graph Neural Networks With Lifting-Based Adaptive Graph Wavelets." IEEE Transactions on Signal and Information Processing over Networks 8 (2022): 63–77. http://dx.doi.org/10.1109/tsipn.2022.3140477.

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Tay, D. B. H., and Z. Lin. "Highly localised near orthogonal graph wavelets." Electronics Letters 52, no. 11 (May 2016): 966–68. http://dx.doi.org/10.1049/el.2016.0482.

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Tremblay, Nicolas, and Pierre Borgnat. "Graph Wavelets for Multiscale Community Mining." IEEE Transactions on Signal Processing 62, no. 20 (October 2014): 5227–39. http://dx.doi.org/10.1109/tsp.2014.2345355.

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Masoumi, Majid, and A. Ben Hamza. "Shape classification using spectral graph wavelets." Applied Intelligence 47, no. 4 (June 9, 2017): 1256–69. http://dx.doi.org/10.1007/s10489-017-0955-7.

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Yang, Zhirui, Yulan Hu, Sheng Ouyang, Jingyu Liu, Shuqiang Wang, Xibo Ma, Wenhan Wang, Hanjing Su, and Yong Liu. "WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (March 24, 2024): 9287–95. http://dx.doi.org/10.1609/aaai.v38i8.28781.

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In the existing spectral GNNs, polynomial-based methods occupy the mainstream in designing a filter through the Laplacian matrix. However, polynomial combinations factored by the Laplacian matrix naturally have limitations in message passing (e.g., over-smoothing). Furthermore, most existing spectral GNNs are based on polynomial bases, which struggle to capture the high-frequency parts of the graph spectral signal. Additionally, we also find that even increasing the polynomial order does not change this situation, which means polynomial-based models have a natural deficiency when facing high-frequency signals. To tackle these problems, we propose WaveNet, which aims to effectively capture the high-frequency part of the graph spectral signal from the perspective of wavelet bases through reconstructing the message propagation matrix. We utilize Multi-Resolution Analysis (MRA) to model this question, and our proposed method can reconstruct arbitrary filters theoretically. We also conduct node classification experiments on real-world graph benchmarks and achieve superior performance on most datasets. Our code is available at https://github.com/Bufordyang/WaveNet
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Sun, Qingyun, Jianxin Li, Beining Yang, Xingcheng Fu, Hao Peng, and Philip S. Yu. "Self-Organization Preserved Graph Structure Learning with Principle of Relevant Information." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 4 (June 26, 2023): 4643–51. http://dx.doi.org/10.1609/aaai.v37i4.25587.

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Most Graph Neural Networks follow the message-passing paradigm, assuming the observed structure depicts the ground-truth node relationships. However, this fundamental assumption cannot always be satisfied, as real-world graphs are always incomplete, noisy, or redundant. How to reveal the inherent graph structure in a unified way remains under-explored. We proposed PRI-GSL, a Graph Structure Learning framework guided by the Principle of Relevant Information, providing a simple and unified framework for identifying the self-organization and revealing the hidden structure. PRI-GSL learns a structure that contains the most relevant yet least redundant information quantified by von Neumann entropy and Quantum Jensen Shannon divergence. PRI-GSL incorporates the evolution of quantum continuous walk with graph wavelets to encode node structural roles, showing in which way the nodes interplay and self-organize with the graph structure. Extensive experiments demonstrate the superior effectiveness and robustness of PRI-GSL.
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Dissertations / Theses on the topic "Graph wavelets"

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Behjat, Hamid. "Statistical Parametric Mapping of fMRI data using Spectral Graph Wavelets." Thesis, Linköpings universitet, Medicinsk informatik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-81143.

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In typical statistical parametric mapping (SPM) of fMRI data, the functional data are pre-smoothed using a Gaussian kernel to reduce noise at the cost of losing spatial specificity. Wavelet approaches have been incorporated in such analysis by enabling an efficient representation of the underlying brain activity through spatial transformation of the original, un-smoothed data; a successful framework is the wavelet-based statistical parametric mapping (WSPM) which enables integrated wavelet processing and spatial statistical testing. However, in using the conventional wavelets, the functional data are considered to lie on a regular Euclidean space, which is far from reality, since the underlying signal lies within the complex, non rectangular domain of the cerebral cortex. Thus, using wavelets that function on more complex domains such as a graph holds promise. The aim of the current project has been to integrate a recently developed spectral graph wavelet transform as an advanced transformation for fMRI brain data into the WSPM framework. We introduce the design of suitable weighted and un-weighted graphs which are defined based on the convoluted structure of the cerebral cortex. An optimal design of spatially localized spectral graph wavelet frames suitable for the designed large scale graphs is introduced. We have evaluated the proposed graph approach for fMRI analysis on both simulated as well as real data. The results show a superior performance in detecting fine structured, spatially localized activation maps compared to the use of conventional wavelets, as well as normal SPM. The approach is implemented in an SPM compatible manner, and is included as an extension to the WSPM toolbox for SPM.
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Júnior, Alcebíades Dal Col. "Visual analytics via graph signal processing." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-22102018-112358/.

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The classical wavelet transform has been widely used in image and signal processing, where a signal is decomposed into a combination of basis signals. By analyzing the individual contribution of the basis signals, one can infer properties of the original signal. This dissertation presents an overview of the extension of the classical signal processing theory to graph domains. Specifically, we review the graph Fourier transform and graph wavelet transforms both of which based on the spectral graph theory, and explore their properties through illustrative examples. The main features of the spectral graph wavelet transforms are presented using synthetic and real-world data. Furthermore, we introduce in this dissertation a novel method for visual analysis of dynamic networks, which relies on the graph wavelet theory. Dynamic networks naturally appear in a multitude of applications from different domains. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. Our method enables the automatic analysis of a signal defined on the nodes of a network, making viable the detection of network properties. Specifically, we use a fast approximation of the graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The wavelet coefficients naturally encode spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This method allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using different scenarios and comparisons involving real dynamic networks.
A transformada wavelet clássica tem sido amplamente usada no processamento de imagens e sinais, onde um sinal é decomposto em uma combinação de sinais de base. Analisando a contribuição individual dos sinais de base, pode-se inferir propriedades do sinal original. Esta tese apresenta uma visão geral da extensão da teoria clássica de processamento de sinais para grafos. Especificamente, revisamos a transformada de Fourier em grafo e as transformadas wavelet em grafo ambas fundamentadas na teoria espectral de grafos, e exploramos suas propriedades através de exemplos ilustrativos. As principais características das transformadas wavelet espectrais em grafo são apresentadas usando dados sintéticos e reais. Além disso, introduzimos nesta tese um método inovador para análise visual de redes dinâmicas, que utiliza a teoria de wavelets em grafo. Redes dinâmicas aparecem naturalmente em uma infinidade de aplicações de diferentes domínios. Analisar e explorar redes dinâmicas a fim de entender e detectar padrões e fenômenos é desafiador, fomentando o desenvolvimento de novas metodologias, particularmente no campo de análise visual. Nosso método permite a análise automática de um sinal definido nos vértices de uma rede, tornando possível a detecção de propriedades da rede. Especificamente, usamos uma aproximação da transformada wavelet em grafo para obter um conjunto de coeficientes wavelet, que são então usados para identificar padrões de atividade em redes de grande porte, incluindo a sua recorrência temporal. Os coeficientes wavelet naturalmente codificam variações espaciais e temporais do sinal, criando uma representação eficiente e com significado expressivo. Esse método permite explorar a evolução estrutural da rede e seus padrões ao longo do tempo. A eficácia da nossa abordagem é demonstrada usando diferentes cenários e comparações envolvendo redes dinâmicas reais.
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Valdivia, Paola Tatiana Llerena. "Graph signal processing for visual analysis and data exploration." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-15102018-165426/.

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Signal processing is used in a wide variety of applications, ranging from digital image processing to biomedicine. Recently, some tools from signal processing have been extended to the context of graphs, allowing its use on irregular domains. Among others, the Fourier Transform and the Wavelet Transform have been adapted to such context. Graph signal processing (GSP) is a new field with many potential applications on data exploration. In this dissertation we show how tools from graph signal processing can be used for visual analysis. Specifically, we proposed a data filtering method, based on spectral graph filtering, that led to high quality visualizations which were attested qualitatively and quantitatively. On the other hand, we relied on the graph wavelet transform to enable the visual analysis of massive time-varying data revealing interesting phenomena and events. The proposed applications of GSP to visually analyze data are a first step towards incorporating the use of this theory into information visualization methods. Many possibilities from GSP can be explored by improving the understanding of static and time-varying phenomena that are yet to be uncovered.
O processamento de sinais é usado em uma ampla variedade de aplicações, desde o processamento digital de imagens até a biomedicina. Recentemente, algumas ferramentas do processamento de sinais foram estendidas ao contexto de grafos, permitindo seu uso em domínios irregulares. Entre outros, a Transformada de Fourier e a Transformada Wavelet foram adaptadas nesse contexto. O Processamento de Sinais em Grafos (PSG) é um novo campo com muitos aplicativos potenciais na exploração de dados. Nesta dissertação mostramos como ferramentas de processamento de sinal gráfico podem ser usadas para análise visual. Especificamente, o método de filtragem de dados porposto, baseado na filtragem de grafos espectrais, levou a visualizações de alta qualidade que foram atestadas qualitativa e quantitativamente. Por outro lado, usamos a transformada de wavelet em grafos para permitir a análise visual de dados massivos variantes no tempo, revelando fenômenos e eventos interessantes. As aplicações propostas do PSG para analisar visualmente os dados são um primeiro passo para incorporar o uso desta teoria nos métodos de visualização da informação. Muitas possibilidades do PSG podem ser exploradas melhorando a compreensão de fenômenos estáticos e variantes no tempo que ainda não foram descobertos.
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Sharpnack, James. "Graph Structured Normal Means Inference." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/246.

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This thesis addresses statistical estimation and testing of signals over a graph when measurements are noisy and high-dimensional. Graph structured patterns appear in applications as diverse as sensor networks, virology in human networks, congestion in internet routers, and advertising in social networks. We will develop asymptotic guarantees of the performance of statistical estimators and tests, by stating conditions for consistency by properties of the graph (e.g. graph spectra). The goal of this thesis is to demonstrate theoretically that by exploiting the graph structure one can achieve statistical consistency in extremely noisy conditions. We begin with the study of a projection estimator called Laplacian eigenmaps, and find that eigenvalue concentration plays a central role in the ability to estimate graph structured patterns. We continue with the study of the edge lasso, a least squares procedure with total variation penalty, and determine combinatorial conditions under which changepoints (edges across which the underlying signal changes) on the graph are recovered. We will shift focus to testing for anomalous activations in the graph, using the scan statistic relaxations, the spectral scan statistic and the graph ellipsoid scan statistic. We will also show how one can form a decomposition of the graph from a spanning tree which will lead to a test for activity in the graph. This will lead to the construction of a spanning tree wavelet basis, which can be used to localize activations on the graph.
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Leandro, Jorge de Jesus Gomes. "Análise de formas usando wavelets em grafos." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-02072014-150049/.

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O presente texto descreve a tese de doutorado intitulada Análise de Formas usando Wavelets em Grafos. O tema está relacionado à área de Visão Computacional, particularmente aos tópicos de Caracterização, Descrição e Classificação de Formas. Dentre os métodos da extensa literatura em Análise de Formas 2D, percebe-se uma presença menor daqueles baseados em grafos com topologia arbitrária e irregular. As contribuições desta tese procuram preencher esta lacuna. É proposta uma metodologia baseada no seguinte pipeline : (i) Amostragem da forma, (ii) Estruturação das amostras em grafos, (iii) Função-base definida nos vértices, (iv) Análise multiescala de grafos por meio da Transformada Wavelet Espectral em grafos, (v) Extração de Características da Transformada Wavelet e (vi) Discriminação. Para cada uma das etapas (i), (ii), (iii), (v) e (vi), são inúmeras as abordagens possíveis. Um dos desafios é encontrar uma combinação de abordagens, dentre as muitas alternativas, que resulte em um pipeline eficaz para nossos propósitos. Em particular, para a etapa (iii), dado um grafo que representa uma forma, o desafio é identificar uma característica associada às amostras que possa ser definida sobre os vértices do grafo. Esta característica deve capturar a influência subjacente da estrutura combinatória de toda a rede sobre cada vértice, em diversas escalas. A Transformada Wavelet Espectral sobre os Grafos revelará esta influência subjacente em cada vértice. São apresentados resultados obtidos de experimentos usando formas 2D de benchmarks conhecidos na literatura, bem como de experimentos de aplicações em astronomia para análise de formas de galáxias do Sloan Digital Sky Survey não-rotuladas e rotuladas pelo projeto Galaxy Zoo 2 , demonstrando o sucesso da técnica proposta, comparada a abordagens clássicas como Transformada de Fourier e Transformada Wavelet Contínua 2D.
This document describes the PhD thesis entitled Shape Analysis by using Wavelets on Graphs. The addressed theme is related to Computer Vision, particularly to the Characterization, Description and Classication topics. Amongst the methods presented in an extensive literature on Shape Analysis 2D, it is perceived a smaller presence of graph-based methods with arbitrary and irregular topologies. The contributions of this thesis aim at fullling this gap. A methodology based on the following pipeline is proposed: (i) Shape sampling, (ii) Samples structuring in graphs, (iii) Function dened on vertices, (iv) Multiscale analysis of graphs through the Spectral Wavelet Transform, (v) Features extraction from the Wavelet Transforms and (vi) Classication. For the stages (i), (ii), (iii), (v) and (vi), there are numerous possible approaches. One great challenge is to nd a proper combination of approaches from the several available alternatives, which may be able to yield an eective pipeline for our purposes. In particular, for the stage (iii), given a graph representing a shape, the challenge is to identify a feature, which may be dened over the graph vertices. This feature should capture the underlying inuence from the combinatorial structure of the entire network over each vertex, in multiple scales. The Spectral Graph Wavelet Transform will reveal such an underpining inuence over each vertex. Yielded results from experiments on 2D benchmarks shapes widely known in literature, as well as results from astronomy applications to the analysis of unlabeled galaxies shapes from the Sloan Digital Sky Survey and labeled galaxies shapes by the Galaxy Zoo 2 Project are presented, demonstrating the achievements of the proposed technique, in comparison to classic approaches such as the 2D Fourier Transform and the 2D Continuous Wavelet Transform.
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Chedemail, Elie. "Débruitage de signaux définis sur des graphes de grande taille avec application à la confidentialité différentielle." Electronic Thesis or Diss., Rennes, École Nationale de la Statistique et de l'Analyse de l'Information, 2023. http://www.theses.fr/2023NSAI0001.

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Au cours de la dernière décennie, le traitement du signal sur graphe est devenu un domaine de recherche très actif. Plus précisément, le nombre d’applications utilisant des repères construits à partir de graphes, tels que les ondelettes sur graphe, a augmenté de manière significative. Nous considérons en particulier le débruitage de signaux sur graphes au moyen d’une décomposition dans un repère ajusté d’ondelettes. Cette approche est basée sur le seuillage des coefficients d’ondelettes à l’aide de l’estimateur sans biais du risque de Stein (SURE). Nous étendons cette méthodologie aux graphes de grande taille en utilisant l’approximation par polynômes de Chebyshev qui permet d’éviter la décomposition de la matrice laplacienne du graphe. La principale difficulté est le calcul de poids dans l’expression du SURE faisant apparaître un terme de covariance en raison de la nature surcomplète du repère d’ondelettes. Le calcul et le stockage de celui-ci est donc nécessaire et rédhibitoire à grande échelle. Pour estimer cette covariance, nous développons et analysons un estimateur de Monte-Carlo reposant sur la transformation rapide de signaux aléatoires. Cette nouvelle méthode de débruitage trouve une application naturelle en confidentialité différentielle dont l’objectif est de protéger les données sensibles utilisées par les algorithmes. Une évaluation expérimentale de ses performances est réalisée sur des graphes de taille variable à partir de données réelles et simulées
Over the last decade, signal processing on graphs has become a very active area of research. Specifically, the number of applications using frames built from graphs, such as wavelets on graphs, has increased significantly. We consider in particular signal denoising on graphs via a wavelet tight frame decomposition. This approach is based on the thresholding of the wavelet coefficients using Stein’s unbiased risk estimate (SURE). We extend this methodology to large graphs using Chebyshev polynomial approximation, which avoids the decomposition of the graph Laplacian matrix. The main limitation is the computation of weights in the SURE expression, which includes a covariance term due to the overcomplete nature of the wavelet frame. The computation and storage of the latter is therefore necessary and impractical for large graphs. To estimate such covariance, we develop and analyze a Monte Carlo estimator based on the fast transform of random signals. This new denoising methodology finds a natural application in differential privacy whose purpose is to protect sensitive data used by algorithms. An experimental evaluation of its performance is carried out on graphs of varying size, using real and simulated data
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IRFAN, MUHAMMAD ABEER. "Joint geometry and color denoising for 3D point clouds." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2912976.

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Tremblay, Nicolas. "Réseaux et signal : des outils de traitement du signal pour l'analyse des réseaux." Thesis, Lyon, École normale supérieure, 2014. http://www.theses.fr/2014ENSL0938/document.

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Cette thèse propose de nouveaux outils adaptés à l'analyse des réseaux : sociaux, de transport, de neurones, de protéines, de télécommunications... Ces réseaux, avec l'essor de certaines technologies électroniques, informatiques et mobiles, sont de plus en plus mesurables et mesurés ; la demande d'outils d'analyse assez génériques pour s'appliquer à ces réseaux de natures différentes, assez puissants pour gérer leur grande taille et assez pertinents pour en extraire l'information utile, augmente en conséquence. Pour répondre à cette demande, une grande communauté de chercheurs de différents horizons scientifiques concentre ses efforts sur l'analyse des graphes, des outils mathématiques modélisant la structure relationnelle des objets d'un réseau. Parmi les directions de recherche envisagées, le traitement du signal sur graphe apporte un éclairage prometteur sur la question : le signal n'est plus défini comme en traitement du signal classique sur une topologie régulière à n dimensions, mais sur une topologie particulière définie par le graphe. Appliquer ces idées nouvelles aux problématiques concrètes d'analyse d'un réseau, c'est ouvrir la voie à une analyse solidement fondée sur la théorie du signal. C'est précisément autour de cette frontière entre traitement du signal et science des réseaux que s'articule cette thèse, comme l'illustrent ses deux principales contributions. D'abord, une version multiéchelle de détection de communautés dans un réseau est introduite, basée sur la définition récente des ondelettes sur graphe. Puis, inspirée du concept classique de bootstrap, une méthode de rééchantillonnage de graphes est proposée à des fins d'estimation statistique
This thesis describes new tools specifically designed for the analysis of networks such as social, transportation, neuronal, protein, communication networks... These networks, along with the rapid expansion of electronic, IT and mobile technologies are increasingly monitored and measured. Adapted tools of analysis are therefore very much in demand, which need to be universal, powerful, and precise enough to be able to extract useful information from very different possibly large networks. To this end, a large community of researchers from various disciplines have concentrated their efforts on the analysis of graphs, well define mathematical tools modeling the interconnected structure of networks. Among all the considered directions of research, graph signal processing brings a new and promising vision : a signal is no longer defined on a regular n-dimensional topology, but on a particular topology defined by the graph. To apply these new ideas on the practical problems of network analysis paves the way to an analysis firmly rooted in signal processing theory. It is precisely this frontier between signal processing and network science that we explore throughout this thesis, as shown by two of its major contributions. Firstly, a multiscale version of community detection in networks is proposed, based on the recent definition of graph wavelets. Then, a network-adapted bootstrap method is introduced, that enables statistical estimation based on carefully designed graph resampling schemes
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Zheng, Xuebin. "Wavelet-based Graph Neural Networks." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/27989.

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This thesis focuses on spectral-based graph neural networks (GNNs). In Chapter 2, we use multiresolution Haar-like wavelets to design a framework of GNNs which equips with graph convolution and pooling strategies. The resulting model is called MathNet whose wavelet transform matrix is constructed with a coarse-grained chain. So our proposed MathNet not only enjoys the multiresolution analysis from the Haar-like wavelets but also leverages the clustering information of the graph data. Furthermore, we develop a novel multiscale representation system for graph data, called decimated framelets, which form a localized tight frame on the graph in Chapter 3. Based on this, we establish decimated G-framelet transforms for the decomposition and reconstruction of the graph data at multi resolutions via a constructive data-driven filter bank. The graph framelets are built on a chain-based orthonormal basis that supports fast graph Fourier transforms. From this, we give a fast algorithm for the decimated G-framelet transforms, or FGT, that has linear computational complexity O (N) for a graph of size N. Finally, in Chapter 4, we present a new approach for assembling graph neural networks based on the undecimated framelet transforms which provide a multiscale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines an undecimated-framelet-based graph convolution UFGConv. The framelet decomposition naturally induces a graph pooling strategy UFGPool by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. Moreover, we propose shrinkage as a new activation for UFGConv, which thresholds the high-frequency information at different scales.
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Kotzagiannidis, Madeleine S. "From spline wavelet to sampling theory on circulant graphs and beyond : conceiving sparsity in graph signal processing." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/56614.

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Graph Signal Processing (GSP), as the field concerned with the extension of classical signal processing concepts to the graph domain, is still at the beginning on the path toward providing a generalized theory of signal processing. As such, this thesis aspires to conceive the theory of sparse representations on graphs by traversing the cornerstones of wavelet and sampling theory on graphs. Beginning with the novel topic of graph spline wavelet theory, we introduce families of spline and e-spline wavelets, and associated filterbanks on circulant graphs, which lever- age an inherent vanishing moment property of circulant graph Laplacian matrices (and their parameterized generalizations), for the reproduction and annihilation of (exponen- tial) polynomial signals. Further, these families are shown to provide a stepping stone to generalized graph wavelet designs with adaptive (annihilation) properties. Circulant graphs, which serve as building blocks, facilitate intuitively equivalent signal processing concepts and operations, such that insights can be leveraged for and extended to more complex scenarios, including arbitrary undirected graphs, time-varying graphs, as well as associated signals with space- and time-variant properties, all the while retaining the focus on inducing sparse representations. Further, we shift from sparsity-inducing to sparsity-leveraging theory and present a novel sampling and graph coarsening framework for (wavelet-)sparse graph signals, inspired by Finite Rate of Innovation (FRI) theory and directly building upon (graph) spline wavelet theory. At its core, the introduced Graph-FRI-framework states that any K-sparse signal residing on the vertices of a circulant graph can be sampled and perfectly reconstructed from its dimensionality-reduced graph spectral representation of minimum size 2K, while the structure of an associated coarsened graph is simultaneously inferred. Extensions to arbitrary graphs can be enforced via suitable approximation schemes. Eventually, gained insights are unified in a graph-based image approximation framework which further leverages graph partitioning and re-labelling techniques for a maximally sparse graph wavelet representation.
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Books on the topic "Graph wavelets"

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Tree structured function estimation with Haar wavelets. Hamburg: Verlag Dr. Kovač, 1999.

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Harmonic Analysis. American Mathematical Society, 2018.

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Book chapters on the topic "Graph wavelets"

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Farsi, Carla, Elizabeth Gillaspy, Sooran Kang, and Judith Packer. "Wavelets and Graph C ∗-Algebras." In Excursions in Harmonic Analysis, Volume 5, 35–86. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54711-4_3.

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Gong, Bo, Benjamin Schullcke, Sabine Krueger-Ziolek, and Knut Moeller. "EIT Imaging Regularization Based on Spectral Graph Wavelets." In XIV Mediterranean Conference on Medical and Biological Engineering and Computing 2016, 1280–84. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32703-7_245.

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Masoumi, Majid, Mahsa Rezaei, and A. Ben Hamza. "Shape Analysis of Carpal Bones Using Spectral Graph Wavelets." In Signals and Communication Technology, 419–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03574-7_12.

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Kuncheva, Zhana, and Giovanni Montana. "Multi-scale Community Detection in Temporal Networks Using Spectral Graph Wavelets." In Personal Analytics and Privacy. An Individual and Collective Perspective, 139–54. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-71970-2_12.

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Rustamov, Raif M., and Leonidas J. Guibas. "Wavelets on Graphs via Deep Learning." In Signals and Communication Technology, 207–22. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03574-7_5.

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Yadav, Rakesh Kumar, Abhishek, Prashant Shukla, Neelanjana Jaiswal, Brijesh Kumar Chaurasia, and Shekhar Verma. "Graph Convolutional Neural Network Using Wavelet Transform." In Communications in Computer and Information Science, 223–36. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-8896-6_18.

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Cioacă, Teodor, Bogdan Dumitrescu, and Mihai-Sorin Stupariu. "Graph-Based Wavelet Multiresolution Modeling of Multivariate Terrain Data." In Signals and Communication Technology, 479–507. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03574-7_15.

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Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "The Spectral Graph Wavelet Transform: Fundamental Theory and Fast Computation." In Signals and Communication Technology, 141–75. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03574-7_3.

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Li, Xin, and Hui Li. "Research on Bearing Fault Feature Extraction Based on Graph Wavelet." In Intelligent Computing Theories and Application, 208–20. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13870-6_17.

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Lürig, Christoph, Roberto Grosso, and Thomas Ertl. "Combining Wavelet Transform and Graph Theory for Feature Extraction and Visualization." In Eurographics, 105–14. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-6876-9_10.

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Conference papers on the topic "Graph wavelets"

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Teimury, Fatemeh, Soumyasundar Pal, Arezou Amini, and Mark Coates. "Estimation of time-series on graphs using Bayesian graph convolutional neural networks." In Wavelets and Sparsity XVIII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2019. http://dx.doi.org/10.1117/12.2530046.

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Li, Haotian, and Naoki Saito. "Metrics of graph Laplacian eigenvectors." In Wavelets and Sparsity XVIII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2019. http://dx.doi.org/10.1117/12.2528644.

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Petrovic, Miljan, and Dimitri Van De Ville. "Slepian guided filtering of graph signals." In Wavelets and Sparsity XVIII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2019. http://dx.doi.org/10.1117/12.2528827.

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Balan, Radu V., and Naveed Haghani. "Discrete optimizations using graph convolutional networks." In Wavelets and Sparsity XVIII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2019. http://dx.doi.org/10.1117/12.2529432.

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Achard, Sophie, Pierre Borgnat, Irène Gannaz, and Marine Roux. "Wavelet-based graph inference using multiple testing." In Wavelets and Sparsity XVIII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2019. http://dx.doi.org/10.1117/12.2529193.

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Girault, Benjamin, Shrikanth S. Narayanan, and Antonio Ortega. "Local stationarity of graph signals: insights and experiments." In Wavelets and Sparsity XVII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2017. http://dx.doi.org/10.1117/12.2274584.

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Cloninger, Alexander. "Prediction models for graph-linked data with localized regression." In Wavelets and Sparsity XVII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2017. http://dx.doi.org/10.1117/12.2271840.

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Silva, Arlei, Xuan Hong Dang, Prithwish Basu, Ambuj Singh, and Ananthram Swami. "Graph Wavelets via Sparse Cuts." In KDD '16: The 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2939672.2939777.

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Ramchandran, Kannan. "Speeding up sparse signal recovery using sparse-graph codes (Conference Presentation)." In Wavelets and Sparsity XVII, edited by Yue M. Lu, Manos Papadakis, and Dimitri Van De Ville. SPIE, 2017. http://dx.doi.org/10.1117/12.2281055.

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Kotzagiannidis, Madeleine S., and Pier Luigi Dragotti. "Higher-order graph wavelets and sparsity on circulant graphs." In SPIE Optical Engineering + Applications, edited by Manos Papadakis, Vivek K. Goyal, and Dimitri Van De Ville. SPIE, 2015. http://dx.doi.org/10.1117/12.2192003.

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Reports on the topic "Graph wavelets"

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Crovella, Mark, and Eric Kolaczyk. Graph Wavelets for Spatial Traffic Analysis. Fort Belvoir, VA: Defense Technical Information Center, July 2002. http://dx.doi.org/10.21236/ada442573.

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AWARE INC CAMBRIDGE MA. The Performance of Wavelets for Data Compression in Selected Military Applications. Volume 2. Supplementary Tables and Graphs. Fort Belvoir, VA: Defense Technical Information Center, January 1990. http://dx.doi.org/10.21236/ada219231.

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