Gaussian Process Landmarking on Manifolds

DOI10.1137/18M1184035zbMath1499.60114arXiv1802.03479OpenAlexW2963122501MaRDI QIDQ5025781

Ingrid Daubechies, Tingran Gao, Shahar Z. Kovalsky

Publication date: 3 February 2022

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

Full work available at URL: https://arxiv.org/abs/1802.03479

zbMATH Keywords

Gaussian processactive learningmanifold learningreduced basis methodsexperimental designgeometric morphometrics

Mathematics Subject Classification ID

Gaussian processes (60G15) Optimal statistical designs (62K05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items

Nyström landmark sampling and regularized Christoffel functions, Unnamed Item, The diffusion geometry of fibre bundles: horizontal diffusion maps, Optimization on Manifolds via Graph Gaussian Processes, The geometry of synchronization problems and learning group actions, Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds, A statistical pipeline for identifying physical features that differentiate classes of 3D shapes, Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics

Uses Software

• mctoolbox
• PCL

Cites Work

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• Bayesian manifold regression
• Embedding Riemannian manifolds by the heat kernel of the connection Laplacian
• On the low-rank approximation by the pivoted Cholesky decomposition
• Two complexity results on \(c\)-optimality in experimental design
• Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
• On selecting a maximum volume sub-matrix of a matrix and related problems
• Clustering to minimize the maximum intercluster distance
• Generalized Procrustes analysis
• Embedding Riemannian manifolds by their heat kernel
• Average-case analysis of numerical problems
• Bayesian experimental design: A review
• The design and analysis of computer experiments
• Minimal Riesz energy point configurations for rectifiable \(d\)-dimensional manifolds
• Extrinsic Gaussian processes for regression and classification on manifolds
• Greedy algorithms for reduced bases in Banach spaces
• Landmark diffusion maps (L-dMaps): accelerated manifold learning out-of-sample extension
• Thomas Bayes' walk on manifolds
• Diffusion maps
• From graph to manifold Laplacian: the convergence rate
• A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
• Submodularity and Randomized rounding techniques for Optimal Experimental Design
• Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
• Vector diffusion maps and the connection Laplacian
• Randomized Rounding for the Largest Simplex Problem
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• Convergence Rates for Greedy Algorithms in Reduced Basis Methods
• Uncertainty Quantification in Graph-Based Classification of High Dimensional Data
• Robust Geometry Estimation Using the Generalized Voronoi Covariance Measure
• Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh
• Volume of a small Extrinsic Ball in a Submanifold
• Local error estimates for radial basis function interpolation of scattered data
• Procrustes Problems
• On the Relative Importance of Input Factors in Mathematical Models
• The geometry of point particles
• On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models
• Accuracy and Stability of Numerical Algorithms
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Probabilistic Sensitivity Analysis of Complex Models: A Bayesian Approach
• Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝ^d
• Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics
• Statistics for Spatial Data
• Optimal Design of Experiments
• Restricted delaunay triangulations and normal cycle
• Faster Subset Selection for Matrices and Applications
• Learning Theory
• Theory of Reproducing Kernels
• Introduction to nonparametric estimation
• Scattered Data Approximation