Geometric scattering on measure spaces

DOI10.1016/j.acha.2024.101635arXiv2208.08561OpenAlexW4391664411MaRDI QIDQ6122637

Matthew J. Hirn, Joyce Chew, Holly Steach, Smita Krishnaswamy, Hau-Tieng Wu, Siddharth Viswanath, Deanna Needell, Michael Perlmutter

Publication date: 1 March 2024

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.08561

zbMATH Keywords

manifold learninggeometric deep learningscattering transformsstability and invariance

Mathematics Subject Classification ID

Biology and other natural sciences (92-XX) Computer science (68-XX)

Cites Work

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• Orientability and diffusion maps
• Wavelets on graphs via spectral graph theory
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Laplacians and the Cheeger inequality for directed graphs
• Spectral convergence of graph Laplacian and heat kernel reconstruction in \(L^\infty\) from random samples
• Improved spectral convergence rates for graph Laplacians on \(\varepsilon \)-graphs and \(k\)-NN graphs
• Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
• Graph convolutional neural networks via scattering
• Gaussian bandwidth selection for manifold learning and classification
• Multiscale sparse microcanonical models
• A note on Markov normalized magnetic eigenmaps
• Magnetic eigenmaps for the visualization of directed networks
• Analysis of time-frequency scattering transforms
• Diffusion maps
• Diffusion wavelets
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary
• Spectral analysis of weighted Laplacians arising in data clustering
• Vector diffusion maps and the connection Laplacian
• Group Invariant Scattering
• A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction
• CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Balancing Geometry and Density: Path Distances on High-Dimensional Data
• Characterization and comparison of large directed networks through the spectra of the magnetic Laplacian
• Hodge Laplacians on Graphs
• Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs

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