Multiscale Wavelets on Trees, Graphs and High Dimensional Data: Theory and Applications to Semi Supervised Learning

By Matan Gavish, Boaz Nadler, Ronald R. Coifman. 2010

245 citations recorded by the source corpus.

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In Graph Learning

Citations in the corpus

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, methodology): “In this context, the authors of [12, 8, 10] revisited the construction of wavelet operators on graphs and techniques to perform mutli-scale pyramid transforms on graphs were proposed in [32, 27].”
Spectral Networks and Locally Connected Networks on Graphs (2013, background): “There is a large literature on building wavelets on graphs, see for example [21, 7, 4, 5, 9].”
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, methodology): “[47]. Spectral analysis techniques were extended to graphs considering the orthogonal eigenfunctions of the Laplacian operator as a generalization of the Fourier basis. Constructions such as wavelets [14, 18, 21, 39, 45] or algorithms such as dictionary learning [62], Lasso [9], PCA [43, 44], or mat”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “Several bottom-up wavelet constructions on graphs were studied in [85] and [86].”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “Examples of vertex domain designs include random transforms [55], graph wavelets [53], lifting based wavelets [49], [61], [62], and tree wavelets [57].”
Wavelets on Graphs via Deep Learning (2013, methodology): “A number of approaches for constructing wavelets on graphs have been proposed, including, but not limited to the CKWT [7], Haar-like wavelets [24, 10], diffusion wavelets [6], spectral wavelets [12], tree-based wavelets [19], average-interpolating wavelets [21], and separable filterbank wavelets [17”
Wavelet-regularized graph semi-supervised learning (2013, background): “This has been the focus of some recent literature [3] [7] [8].”
Generalized Tree-Based Wavelet Transform (2010, methodology): “For the case of more general trees and Haar like bases, the reader may refer to [1].”
Learning Laplacian Matrix in Smooth Graph Signal Representations (2014, background): “We believe that our new framework can benefit numerous emerging real world applications, such as the analysis of transportation, biomedical, and social networks, where it is critical to infer hidden relationships between data entities.”
A class of Laplacian multiwavelets bases for high-dimensional data (2015, methodology): “The family of bases is parameterized by one integer parameter 1 ≤ k ≤ N , where k = 1 corresponds to the Haar basis defined in [24], and k = N corresponds to the eigenvectors of the graph Laplacian (Fourier basis).”
Deep Haar Scattering Networks (2015, methodology): “A tree representation of graph data defines a multi-resolution analysis associated to a Haar wavelet basis [10,16].”
Unsupervised Deep Haar Scattering on Graphs (2014, background): “Haar wavelet transforms are flexible representations which characterize multiscale signal patterns on graphs [6, 10, 11].”
Image denoising with nonlocal spectral graph wavelets (2010, background): “have recently described an orthogonal wavelet construction on hierarchical trees, and demonstrated its use for estimating functions on arbitrary graphs by first applying hierarchical clustering of nodes [17].”
Relational Graph Attention Networks (2018, background): “Hybrid approaches combine spectral and spatial approaches, trading their advantages and deficiencies against each-other (Bronstein et al., 2017; Rustamov and Guibas, 2013; Szlam et al., 2005; Gavish et al., 2010).”
Data-Driven Tree Transforms and Metrics (2017, methodology): “Various methodologies have been proposed for the construction of wavelets on graphs, including Haar wavelets, and wavelets based on spectral clustering and spanning tree decompositions [13]–[16], [26], [27].”