Diffusion Wavelets

By Ronald R. Coifman, Mauro Maggioni. 2004

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Citations in the corpus

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): “Constructions such as wavelets [14, 18, 21, 39, 45] or algorithms such as dictionary learning [62], Lasso [9], PCA [43, 44], or matrix completion [23] originally developed for the Euclidean domain, were also applied to graph-structured data.”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “Wavelets have been extensively studied in general graph domains [84].”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “Notable examples in this category include diffusion wavelets [24], [44], spectral graph wavelets [41], and graph quadrature mirror ﬁlter banks (graph-QMF ﬁlter banks) [37].”
Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “[31] used the graph wavelets of Crovella and Kolaczyk as part of a larger method for measuring structural diﬀerences between graphs representing chemical structures, for machine learning of chemical activities for virtual drug screening.”
Learning Laplacian Matrix in Smooth Graph Signal Representations (2014, background): “Representative works include studies on the generalizations of the Fourier transform [9], [10], the wavelet transform [11]–[16], dictionary learning methods [17], [18], and time-frequency analysis [19], [20] on graphs, with applications to image processing [21], brain network classification [22], mo”
Learning Graphs From Data: A Signal Representation Perspective (2018, background): “Examples include the generalization of the Fourier and wavelet transforms for graph signals [13], [46], [47], which are defined based on mathematical properties of a given graph G.”
A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel (2010, methodology): “1 Introduction Many practical applications, for example, document analysis [8], face recognition [17], semi–supervised learning [2, 1], image processing [10], and cataloguing of galaxies [11], involve a large amount of very high dimensional data.”
Discrete Signal Processing on Graphs (2012, methodology): “Examples include regression algorithms [31], wavelet decompositions [30], [32]–[35], filter banks on graphs [36], [37], de-noising [38], and compression [39].”
Diffusion maps (2006, background): “Indeed, the action of operator P and its powers therefore exhibit a multiscale structure of which one can take advantage in order to rapidly compute functions of this operator [16,17].”
Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization (2006, methodology): “Note also that by using different values of t, we are able to perform a multiscale analysis of the data [22], [23].”
Graph spectral image smoothing using the heat kernel (2008, methodology): “The samemeasurement has recently also been used in the graph-based setting for multi-scale image analysis and denoising using diffusion wavelets [26].”
Wavelet transform on manifolds: Old and new approaches (2010, background): “• Diffusion wavelets [12] form an orthogonal basis of wavelet-like functions on a graph.”
Signals on Graphs: Uncertainty Principle and Sampling (2015, background): “Indeed, starting from and multiplying from the left side by B , taking into account that B 2 = B , we get Equating (15) to (16), we get which implies that x is perfectly localized in the frequency domain.”
Wavelet-regularized graph semi-supervised learning (2013, background): “This has been the focus of some recent literature [3] [7] [8].”
Nearly tight frames and space-frequency analysis on compact manifolds (2007, background): “• Coifman, Maggioni, and collaborators ([5], [27]) used the heat equation on manifolds for the rather different purpose of constructing orthonormal wavelet bases through a diffusion process, leading to a multiresolution analysis.”