Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling

DOI10.1137/22m1516968arXiv2209.08004OpenAlexW4384821870MaRDI QIDQ6136229

Xiuyuan Cheng, Boris Landa

Publication date: 29 August 2023

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.08004

zbMATH Keywords

manifold learningdoubly stochasticdiffusion mapsgraph Laplaciannoise robustnessaffinity matrixSinkhorn scaling

Mathematics Subject Classification ID

Nonparametric inference (62Gxx) Statistical aspects of big data and data science (62R07)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computational Optimal Transport: With Applications to Data Science
• On information plus noise kernel random matrices
• Wavelets on graphs via spectral graph theory
• Variable bandwidth diffusion kernels
• Entropy minimization, \(DAD\) problems, and doubly stochastic kernels
• Clipped noisy images: heteroskedastic modeling and practical denoising
• 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
• Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator
• Poisson noise reduction with non-local PCA
• Perturbation of the eigenvectors of the graph Laplacian: application to image denoising
• Role of normalization in spectral clustering for stochastic blockmodels
• Diffusion maps
• Diffusion wavelets
• Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
• From graph to manifold Laplacian: the convergence rate
• Concerning nonnegative matrices and doubly stochastic matrices
• Learning doubly stochastic and nearly idempotent affinity matrix for graph-based clustering
• A common variable minimax theorem for graphs
• Symmetrizing Smoothing Filters
• A Symmetry Preserving Algorithm for Matrix Scaling
• Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denoising
• Remarks on Some Nonparametric Estimates of a Density Function
• Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain
• High-Dimensional Probability
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise
• Spectral Convergence of Diffusion Maps: Improved Error Bounds and an Alternative Normalization
• Manifold learning with bi-stochastic kernels
• Strong uniform consistency with rates for kernel density estimators with general kernels on manifolds
• The Steerable Graph Laplacian and its Application to Filtering Image Datasets
• Analysis of call centre arrival data using singular value decomposition
• Learning Theory
• A Note Concerning Simultaneous Integral Equations
• A Review of Image Denoising Algorithms, with a New One
• On Estimation of a Probability Density Function and Mode
• Graph connection Laplacian methods can be made robust to noise

This page was built for publication: Robust Inference of Manifold Density and Geometry by Doubly Stochastic Scaling