Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions

By Arthur Szlam, Mauro Maggioni, Ronald R. Coifman, James Bremer. 2005

68 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

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In Computational Theory and Mathematics

Citations in the corpus

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): “These include wavelets on unweighted graphs for analyzing computer network traffic [53], diffusion wavelets and diffusion wavelet packets [24], [44], [45], the “topdown” wavelet construction of [54], graph dependent basis functions for sensor network graphs [55], lifting based wavelets on graphs [49”
Nonlocal Operators with Applications to Image Processing (2008, background): “In the more common case where the weights are computed with a Gaussian-like formula, e.g. as in [9],[28],[52],[30], the weights decay fast for distances above a certain threshold (usually related to the noise variance).”
Diffusion Wavelets (2004, background): “Different types of multiscale bases on graphs and manifolds are constructed in [56].”
Nonlocal Linear Image Regularization and Supervised Segmentation (2007, unknown): “The weights can be computed by (see also [52] [57]): g(F f (x), F f (y)) = e −(|F f (x)−F f (y)|/h) 2 , F f (x) = (v 1 , . . . , v M )(x), Ω w (x) = {y ∈ Ω : |y − x| ≤ r}, (2.17) The nonlocal version of Yaroslavsky [62] affinity (in its weighted form) is very similar to (2.15) except that the…”
Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian (2007, background): “The first is that graph eigenfunctions are global objects and any 1 Examples of such disparate applications include document analysis [15], face recognition [26], clustering [37, 1], machine learning [4, 38, 52, 34, 33, 53], nonlinear image denoising and segmentation [45, 52], processing of articula”
A class of Laplacian multiwavelets bases for high-dimensional data (2015, background): “[42] Szlam, A.”
Diffusion polynomial frames on metric measure spaces (2008, methodology): “To the best of our knowledge, the recent construction of diffusion wavelets [15, 24] and other multiscale bases [41] on graphs and manifolds are the first attempts to develop tools for the multiscale analysis on these spaces.”