Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances

DOI10.1051/cocv/2023088arXiv2012.13770OpenAlexW3117439251MaRDI QIDQ6145581

Nikita Puchkin, Dario Trevisan, Eugene Stepanov, Vladimir Spokoiny

Publication date: 2 February 2024

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.13770

zbMATH Keywords

manifold learningmultidimensional scalingmanifold embeddingmaximum variance unfolding

Mathematics Subject Classification ID

Semidefinite programming (90C22) Numerical optimization and variational techniques (65K10) Manifolds and measure-geometric topics (49Q99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Manifold estimation and singular deconvolution under Hausdorff loss
• Random projections of smooth manifolds
• Stability and minimax optimality of tangential Delaunay complexes for manifold reconstruction
• Only distances are required to reconstruct submanifolds
• Nonasymptotic rates for manifold, tangent space and curvature estimation
• Multidimensional scaling on metric measure spaces
• Manifold approximation by moving least-squares projection (MMLS)
• The reach, metric distortion, geodesic convexity and the variation of tangent spaces
• Manifold reconstruction using tangential Delaunay complexes
• Finding the homology of submanifolds with high confidence from random samples
• Multiscale Dictionary Learning: Non-Asymptotic Bounds and Robustness
• Curvature Measures
• Tighter bounds for random projections of manifolds
• Infinite multidimensional scaling for metric measure spaces