mlsanityData to 14 Oct 2026

Manifold learning: what, how, and why

arXiv 2311.03757 ↗First posted 7 Nov 2023stat.ML cs.LGcited by 68

Not on the map. Why?

Abstract (arXiv)

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new representations and descriptors obtained by ML reveal the geometric shape of high dimensional point clouds, and allow one to visualize, de-noise and interpret them. This survey presents the principles underlying ML, the representative methods, as well as their statistical foundations from a practicing statistician's perspective. It describes the trade-offs, and what theory tells us about the parameter and algorithmic choices we make in order to obtain reliable conclusions.

Key facts. Cited by 68 papers in the map (data through 14 Oct 2026). Builds on 20 of its 108 references that are in the map. First posted on arXiv 7 Nov 2023.

Builds on

20 of 108 references.

References · 20

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  2. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  3. 2018Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorcited by 70
  4. 2017Clustering with t-SNE, provablycited by 51
  5. 2020Attraction-Repulsion Spectrum in Neighbor Embeddingscited by 41
  6. 2017Analysis of p-Laplacian Regularization in Semi-Supervised Learningcited by 39
  7. 2015A variational approach to the consistency of spectral clusteringcited by 28
  8. 2019Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisationscited by 22
  9. 2021Intrinsic Dimension Estimation Using Wasserstein Distancescited by 20
  10. 2019Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphscited by 18
  11. 2013Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discoverycited by 14
  12. 2021LDLE: Low Distortion Local Eigenmapscited by 11
8 more
  1. 2016Minimax Rates for Estimating the Dimension of a Manifoldcited by 10
  2. 2021t-SNE, Forceful Colorings and Mean Field Limitscited by 10
  3. 2014Asymptotic theory for density ridgescited by 9
  4. 2018Stochastic Neighbor Embedding under f-divergencescited by 9
  5. 2021The decomposition of the higher-order homology embedding constructed from the k-Laplaciancited by 8
  6. 2017Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysiscited by 7
  7. 2014Improved graph Laplacian via geometric self-consistencycited by 5
  8. 2020Manifold Learning via Manifold Deflationcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 10; 2025: 36; 2026: 22.

68 papers.

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  1. 2025Landing with the Score: Riemannian Optimization through Denoisingcited by 8
  2. 2026Staying VIGILant: Mitigating Visual Laziness via Counterfactual Visual Alignment in MLLMscited by 8
  3. 2024Towards aerodynamic surrogate modeling based on β-variational autoencoderscited by 5
  4. 2026DisRFM: Polar Riemannian Flow Matching for Structure-Preserving Graph Domain Adaptationcited by 4
  5. 2024Inductive Global and Local Manifold Approximation and Projectioncited by 3
  6. 2025Adaptive Multi-Order Graph Regularized NMF with Dual Sparsity for Hyperspectral Unmixingcited by 3
  7. 2025GeoDM: Geometry-aware Distribution Matching for Dataset Distillationcited by 3
  8. 2024Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operatorscited by 2
  9. 2024Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservationcited by 2
  10. 2024A review of unsupervised learning in astronomycited by 2
  11. 2024Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniquescited by 2
  12. 2025Adversarial Subspace Generation for Outlier Detection in High-Dimensional Datacited by 2
38 more
  1. 2025Cryo-em images are intrinsically low dimensionalcited by 2
  2. 2025EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddingscited by 2
  3. 2025Learning Reduced Representations for Quantum Classifierscited by 2
  4. 2026The Semantic Bottleneck: Leveraging Semantic Representations for Non-Invasive Speech Decodingcited by 2
  5. 2024Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou High-Dimensional Trajectories Through Manifold Learning: A Linear Approachcited by 1
  6. 2025Structure-preserving contrastive learning for spatial time seriescited by 1
  7. 2025Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operatorscited by 1
  8. 2025Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularizationcited by 1
  9. 2025Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimizationcited by 1
  10. 2025Learnable quantum spectral filters for hybrid graph neural networkscited by 1
  11. 2025Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problemscited by 1
  12. 2025Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detectioncited by 1
  13. 2025Atlas-based Manifold Representations for Interpretable Riemannian Machine Learningcited by 1
  14. 2025Inference for Similarity and Alignability between Noisy High-Dimensional Datasetscited by 1
  15. 2026Exploring Time Conditioning in Diffusion Generative Models from Disjoint Noisy Data Manifoldscited by 1
  16. 2024Datacube segmentation via Deep Spectral Clusteringcited by 0
  17. 2024Strong denoising of financial time-seriescited by 0
  18. 2024Pseudo-Nonlinear Data Augmentation: A Constrained Energy Minimization Viewpointcited by 0
  19. 2025Mask-informed Deep Contrastive Incomplete Multi-view Clusteringcited by 0
  20. 2025Supervised Manifold Learning for Functional Datacited by 0
  21. 2025Analytical Discovery of Manifold with Machine Learningcited by 0
  22. 2025The When and How of Target Variable Transformationscited by 0
  23. 2025IIKL: Isometric Immersion Kernel Learning with Riemannian Manifold for Geometric Preservationcited by 0
  24. 2025Active Learning for Manifold Gaussian Process Regressioncited by 0
  25. 2025TokenBlowUp: Resolving Representational Singularities in LLM Token Spaces via Monoidal Transformationscited by 0
  26. 2025FedMP: Tackling Medical Feature Heterogeneity in Federated Learning from a Manifold Perspectivecited by 0
  27. 2025Optimizing Multi-Modality Trackers via Significance-Regularized Tuningcited by 0
  28. 2025Property-Isometric Variational Autoencoders for Sequence Modeling and Designcited by 0
  29. 2025A Survey and Comparative Evaluation of Intrinsic Dimension Estimators under the Manifold Hypothesiscited by 0
  30. 2025Neighbor Embeddings Using Unbalanced Optimal Transport Metricscited by 0
  31. 2025Recovering Wasserstein Distance Matrices from Few Measurementscited by 0
  32. 2025LAVA: Explainability for Unsupervised Latent Embeddingscited by 0
  33. 2025Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalizationcited by 0
  34. 2025Manifold Dimension Estimation via Local Graph Structurecited by 0
  35. 2025Fast dynamical similarity analysiscited by 0
  36. 2025A Trainable Centrality Framework for Modern Datacited by 0
  37. 2025Noise-robust Contrastive Learning for Critical Transition Detection in Dynamical Systemscited by 0
  38. 2025Multivariate Time Series Forecasting with Hybrid Euclidean-SPD Manifold Graph Neural Networkscited by 0

50 most cited of 68 All 68 (JSON)