Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning

zbMath1498.68221arXiv1810.09569MaRDI QIDQ4969047

Bruno Pelletier, Ery Arias-Castro, Adel Javanmard

Publication date: 5 October 2020

Full work available at URL: https://arxiv.org/abs/1810.09569

zbMATH Keywords

localizationdimensionality reductionmanifold learning

Mathematics Subject Classification ID

Statistics on manifolds (62R30) Learning and adaptive systems in artificial intelligence (68T05) Pattern recognition, speech recognition (68T10)

Related Items (4)

Infinite multidimensional scaling for metric measure spaces ⋮ Universally consistent estimation of the reach ⋮ Localization in 1D non-parametric latent space models from pairwise affinities ⋮ On the estimation of latent distances using graph distances

Uses Software

• kappa_SQ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localization from incomplete noisy distance measurements
• Manifold estimation and singular deconvolution under Hausdorff loss
• Discrete Hessian eigenmaps method for dimensionality reduction
• Tight minimax rates for manifold estimation under Hausdorff loss
• User-friendly tail bounds for sums of random matrices
• Theory of semidefinite programming for sensor network localization
• Towards a theoretical foundation for Laplacian-based manifold methods
• Continuum isomap for manifold learnings
• Perturbation analysis of the orthogonal Procrustes problem
• The solution of orthogonal Procrustes problems for a family of orthogonally invariant norms
• Unconstrained and curvature-constrained shortest-path distances and their approximation
• Consistency of spectral clustering
• Diffusion maps
• From graph to manifold Laplacian: the convergence rate
• Multidimensional scaling. I: Theory and method
• Curvature Measures
• Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results
• The Effect of Coherence on Sampling from Matrices with Orthonormal Columns, and Preconditioned Least Squares Problems
• Randomized Approximation of the Gram Matrix: Exact Computation and Probabilistic Bounds
• Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
• Learning Theory
• Some distance properties of latent root and vector methods used in multivariate analysis

This page was built for publication: Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning