mlsanityData to 14 Oct 2026

Manifold learning in metric spaces

arXiv 2503.16187 ↗First posted 20 Mar 2025cs.LG stat.MLcited by 2

Not on the map. Why?

Abstract (arXiv)

Laplacian-based methods are popular for the dimensionality reduction of data lying in ℝN. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance on the underlying submanifold which the data are assumed to lie on. However, for some applications, other metrics, such as the Wasserstein distance, may provide a more appropriate notion of distance than the Euclidean distance. We provide a framework that generalizes the problem of manifold learning to metric spaces and study when a metric satisfies sufficient conditions for the pointwise convergence of the graph Laplacian.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 25 of its 79 references that are in the map. First posted on arXiv 20 Mar 2025.

Builds on

25 of 79 references.

References · 25

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2018Computational Optimal Transportcited by 780
  3. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 85
  4. 2018Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorcited by 70
  5. 2024Statistical optimal transportcited by 47
  6. 2020Lipschitz regularity of graph Laplacians on random data cloudscited by 26
  7. 2016Wasserstein Discriminant Analysiscited by 25
  8. 2021Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolationcited by 24
  9. 2018Natural gradient via optimal transportcited by 20
  10. 2020Convergence of Graph Laplacian with kNN Self-tuned Kernelscited by 17
  11. 2015Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metriccited by 15
  12. 2022Wassmap: Wasserstein Isometric Mapping for Image Manifold Learningcited by 15
13 more
  1. 2018Optimal transport natural gradient for statistical manifolds with continuous sample spacecited by 14
  2. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  3. 2023Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithmscited by 12
  4. 2015Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discoverycited by 10
  5. 2020Manifold learning with arbitrary normscited by 10
  6. 2016The embedding dimension of Laplacian eigenfunction mapscited by 8
  7. 2019Earthmover-based manifold learning for analyzing molecular conformation spacescited by 8
  8. 2022Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noisecited by 7
  9. 2023Applications of No-Collision Transportation Maps in Manifold Learningcited by 6
  10. 2023Manifold learning in Wasserstein spacecited by 6
  11. 2024A kernel-based analysis of Laplacian Eigenmapscited by 3
  12. 2023Entropic Wasserstein Component Analysiscited by 2
  13. 2023On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomenacited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026K-means with learned metricscited by 0
  2. 2026Group Invariant Spectral Embeddingcited by 0