Manifold Learning

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Manifold learning seeks compact representations of high-dimensional data by modeling it as lying near a lower-dimensional, possibly curved space, enabling visualization, denoising, scientific analysis, and learning with fewer effective degrees of freedom. Common approaches build neighborhood graphs and optimize UMAP- or t-SNE-style embeddings, recover coordinates or operators with spectral and diffusion methods, or use autoencoders with geometric constraints; Riemannian and optimal-transport methods handle structured objects such as covariance matrices and probability distributions. Work increasingly targets properties beyond nearest-neighbor preservation—including density, geodesic distances, topology, tangent spaces, symmetry, and out-of-sample mapping—in settings from images and single-cell data to networks and dynamical systems. A central challenge is balancing local fidelity against global geometry and computational scale, while noise, sparse or anisotropic sampling, and inconsistent evaluation metrics make it difficult to tell when an embedding reflects the underlying manifold.

Latest papers

115 papers10 papers in the last four weeks, up 43% on the four weeks before. 0.1% of all new papers.

Differentially Private Manifold Denoising
Apr 1, 2026Jiaqi Wu, Yiqing Sun, Zhigang YaoPrivacy-Preserving ML Differential Privacy
Department of Statistics and Data Science, National University of Singapore
Denoising distances beyond the volumetric barrier
Apr 1, 2026Han Huang, Pakawut Jiradilok, Elchanan MosselManifold Learning Latent Space Geometry
Diffusion Maps is not Dimensionality Reduction
Mar 30, 2026Julio Candanedo, Alejandro PatiñoManifold Learning Dimensionality Reduction
SparseTrace.ai. Appleton, WI, USA. · Universidad Nacional de Colombia sede Manizales. Manizales, Caldas, Colombia
Accelerate Vector Diffusion Maps by Landmarks
Mar 22, 2026Sing-Yuan Yeh, Yi-An Wu, Hau-Tieng Wu +1Manifold Learning
Continual Learning as Shared-Manifold Continuation Under Compatible Shift
Mar 20, 2026Henry J. KobsContinual Learning Geometric Representation Learning
GeMA: Learning Latent Manifold Frontiers for Benchmarking Complex Systems
Mar 17, 2026Jia Ming Li, Anupriya, Daniel J. GrahamManifold Learning Variational Autoencoders
Transport Strategy Centre, Imperial College London, London, SW7 2AZ, United Kingdom.
Manifold-Matching Autoencoders
Mar 17, 2026Laurent Cheret, Vincent Létourneau, Isar Nejadgholi +3Multidimensional Scaling Autoencoders
Department of Computer Science, University of Ottawa, Ottawa, Canada · MILA, Montréal, Canada · National Research Council of Canada, Ottawa, Canada
Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embedding
Mar 12, 2026Hannah Sansford, Nick Whiteley, Patrick Rubin-DelanchySpectral Graph Embedding Graph Embedding
School of Mathematics, University of Bristol, UK · School of Mathematics, University of Edinburgh, UK
Context-dependent manifold learning: A neuromodulated constrained autoencoder approach
Mar 12, 2026Jérôme Adriaens, Gustave Bainier, Guillaume Drion +1Autoencoders Manifold Learning
Neuroengineering Lab, Department of Electrical Engineering and Computer Science, University of Liège · University of Liège, Liège, Belgium
Harnessing Data Asymmetry: Manifold Learning in the Finsler World
Mar 12, 2026Thomas Dagès, Simon Weber, Daniel Cremers +1Finsler Geometry Manifold Learning
Technion – Israel Institute of Technology · Technical University of Munich · Munich Center for Machine Learning +1
The Theory behind UMAP?
Mar 2, 2026David WegmannCategory Theory Dimensionality Reduction
University of Erlangen-Nuremberg
Manifold Aware Denoising Score Matching (MAD)
Mar 2, 2026Alona Levy-Jurgenson, Alvaro Prat, James Cuin +1Score-Based Generative Modeling Generative Modeling
Department of Statistics University of Oxford · Department of Mathematics, Imperial College London, London, United Kingdom
A Comparative Study of UMAP and Other Dimensionality Reduction Methods
Mar 1, 2026Guanzhe Zhang, Shanshan Ding, Zhezhen JinDimensionality Reduction Manifold Learning
Department of Applied Economics and Statistics, University of Delaware · Department of Biostatistics, Columbia University
Histopathology Image Normalization via Latent Manifold Compaction
Feb 27, 2026Xiaolong Zhang, Jianwei Zhang, Selim Sevim +3Computational Pathology Domain Generalization
Knight Cancer Institute, Oregon Health and Science University, Oregon, USA · Brenden-Colson Center for Pancreatic Care, Oregon Health and Science University, Oregon, USA
Manifold-Preserving Superpixel Hierarchies and Embeddings for the Exploration of High-Dimensional Images
Feb 27, 2026Alexander Vieth, Boudewijn Lelieveldt, Elmar Eisemann +2Hierarchical Representation Learning Dimensionality Reduction
Leiden University Medical Center, Leiden, The Netherlands · Delft University of Technology, Delft, The Netherlands · Eindhoven University of Technology, Eindhoven, The Netherlands
RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs
Feb 26, 2026Haohui Jia, Zheng Chen, Lingwei Zhu +4EEG Decoding Geometric Representation Learning
Information Science and Techinology, Hokkaido University, Japan · SANKEN, The University of Osaka, Japan · Great Bay University, China +1
Learning Tangent Bundles and Characteristic Classes with Autoencoder Atlases
Feb 26, 2026Eduardo Paluzo-Hidalgo, Yuichi IkeManifold Learning Autoencoders
Department of Applied Mathematics I, University of Sevilla, Sevilla, Spain · Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan
Learning Without Training
Feb 20, 2026Ryan O'DowdFunction Approximation Supervised Learning
Claremont Graduate University
Discovering Data Manifold Geometry through Geometric Properties
Feb 2, 2026David Vigouroux, Lucas Drumetz, Ronan Fablet +1Unsupervised Representation Learning Geometric Representation Learning
ANITI, IMT Atlantique - DSD, LaTIM · IRT Saint Exupery, ANITI, Toulouse, France · IMT Atlantique, LaTIM UMR 1101 INSERM, Brest, France +5
Geometry-Aware Deep Congruence Networks for Manifold Learning in Cross-Subject Motor Imagery
Nov 24, 2025Sanjeev Manivannan, Chandra Shekar LakshminarayanCross-Subject EEG Decoding MI Classification
Department of Biotechnology · Department of Data Science and Artificial Intelligence
Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
Oct 2, 2025Dhruv Kohli, Sawyer J. Robertson, Gal Mishne +1Manifold Learning Spectral Methods
HomID : Benchmarking Intrinsic Dimension Estimators on Homogenous Manifolds with Anisotropic Embeddings
Oct 1, 2025Aritra Das, Joseph T. Iosue, Victor V. AlbertIntrinsic Dimensionality Manifold Learning
Joint Center for Quantum Information and Computer Science (QuICS), NIST & UMD College Park. · Joint Quantum Institute (JQI), NIST & UMD College Park.
Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels
May 30, 2025Yi Gu, Antonio AuffingerDimensionality Reduction Manifold Learning
Department of Mathematics, Northwestern University
Manifold meta-learning for reduced-complexity neural system identification
Apr 16, 2025Marco Forgione, Ankush Chakrabarty, Dario Piga +2System Identification Meta-Learning
SUPSI, IDSIA - Dalle Molle Institute for Artificial Intelligence, Lugano, Switzerland. · Mitsubishi Electric Research Laboratories (MERL), Cambridge, MA, USA. · IMT School for Advanced Studies Lucca, Lucca, Italy.
Linearized Wasserstein dimensionality reduction with approximation guarantees
Feb 14, 2023Alexander Cloninger, Keaton Hamm, Varun Khurana +1Dimensionality Reduction Manifold Learning
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CALIFORNIA, SAN DIEGO, CA · HALICIOĦGLU DATA SCIENCE INSTITUTE, UNIVERSITY OF CALIFORNIA, SAN DIEGO, CA · DEPARTMENT OF MATHEMATICS, UNIVERSITY OF TEXAS AT ARLINGTON, ARLINGTON, TX +1

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Differentially Private Manifold Denoising

Jiaqi Wu, Yiqing Sun, Zhigang Yao

Department of Statistics and Data Science, National University of Singapore

Privacy-Preserving ML Differential Privacy Manifold Learning

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We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without compromising privacy. The method follows an iterative procedure that (i) privately estimates local means and tangent geometry using the reference data under calibrated sensitivity, (ii) projects query points along the privately estimated subspace toward the local mean via corrective steps at each iteration, and (iii) performs rigorous privacy accounting across iterations and queries using

(\varepsilon,δ)

-differential privacy (DP). Conceptually, this framework brings differential privacy to manifold methods, retaining sufficient geometric signal for downstream tasks such as embedding, clustering, and visualization, while providing formal DP guarantees for the reference data. Practically, the procedure is modular and scalable, separating DP-protected local geometry (means and tangents) from budgeted query-point updates, with a simple scheduler allocating privacy budget across iterations and queries. Under standard assumptions on manifold regularity, sampling density, and measurement noise, we establish high-probability utility guarantees showing that corrected queries converge toward the manifold at a non-asymptotic rate governed by sample size, noise level, bandwidth, and the privacy budget. Simulations and case studies demonstrate accurate signal recovery under moderate privacy budgets, illustrating clear utility-privacy trade-offs and providing a deployable DP component for manifold-based workflows in regulated environments without reengineering privacy systems.