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Journal articles

Academic literature on the topic 'Graph wavelets'

Author: Grafiati

Published: 18 May 2024

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Journal articles on the topic "Graph wavelets"

1

Wu, Jiasong, Fuzhi Wu, Qihan Yang, et al. "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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2

Hammond, David K., Pierre Vandergheynst, and Rémi Gribonval. "Wavelets on graphs via spectral graph theory." Applied and Computational Harmonic Analysis 30, no. 2 (2011): 129–50. http://dx.doi.org/10.1016/j.acha.2010.04.005.

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3

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 (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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4

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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5

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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6

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

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7

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

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8

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

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9

Yang, Zhirui, Yulan Hu, Sheng Ouyang, et al. "WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (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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10

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 (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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