Dimensionality Reduction

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Overview

Dimensionality reduction turns data with many variables into a smaller representation that is easier to visualize, analyze, store, or use in a predictive model. Linear methods such as PCA and supervised discriminant projections select directions of variation, while t-SNE, UMAP, graph and spectral methods, optimal transport, and autoencoders capture nonlinear structure. Researchers apply these approaches to images, text embeddings, biological data, and dynamical systems, evaluating them through reconstruction, classification, neighborhood, density, and topology preservation. A central tension is that preserving variance or local neighborhoods may discard task-relevant signals or distort global geometry, so methods and evaluations increasingly account for the intended use, uncertainty, and out-of-sample behavior.

Latest papers

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145 papers9 papers in the last four weeks, down 36% on the four weeks before. 0.1% of all new papers.

  1. Sufficient Dimesion Reduction via Generalized Stein's Lemma

    Aug 15, 2026Ye TianDimensionality Reduction

    Key Laboratory of Applied Statistics of MOE, Key Laboratory of Big Data Analysis of Jilin Province, School of Mathematics and Statistics, Northeast Normal University, Renmin Street, Changchun, 130024, Jilin, China

  2. Function Lives Where Variance Doesn't: Task-Weighted Charts of a Language Model's Computation

    Aug 12, 2026Alexandre QuemyRepresentation Geometry in Language ModelsIntrinsic Dimensionality

    Hother, Krak´ow, Poland

  3. When Is a General Factor Distinguishable? Non-Proportionality, Stable Structure, and the Bifactor Decision

    Aug 11, 2026Jinsong ChenLatent Variable ModelsParameter Identifiability

    Faculty of Education, The University of Hong Kong

  4. CosMAP: Contrastive Manifold Approximation and Projection for Dimensionality Reduction of Omics and Genealogical Data

    Aug 11, 2026Fenosoa Randrianjatovo, Maya Saleh, Simon Girard +1Manifold LearningDimensionality Reduction

    Institut national de la recherche scientifique (INRS) · Centre Armand-Frappier Santé Biotechnologie (INRS-AFSB) · Unité mixte de recherche en santé durable (UMR INRS–UQAC) +1

  5. A Convolutional Layer Activation Dimensionality Reduction for Out-of-Distribution and Adversarial Attack Detection Methods

    Aug 10, 2026Leandro de Souza Rosa, Lorenzo Capelli, Clara Nunes Barrancos +2Convolutional Neural NetworksDimensionality Reduction

    Dipartimento di Ingegneria dell’Energia Elettrica e dell’Informazione “Guglielmo Marconi” (DEI) - Alma Mater Studiorum Università di Bologna, Bologna, Italy · Advanced Research Center on Electronic Systems “Ercole De Castro” (ARCES) - Alma Mater Studiorum Università di Bologna, Bologna, Italy

  6. Understanding Differentiable Embeddings Through Differential and Integral Geometry

    Aug 7, 2026Xinyu Zhang, Klaus MuellerDimensionality Reduction

    Stony Brook University · Department of Computer Science, Stony Brook University, Stony Brook, NY, USA

  7. Physics-informed reduced-order modelling with equivariant spectral submanifolds

    Aug 4, 2026Georg MaierhoferReduced-Order ModelingScientific ML

    Department of Applied Mathematics and Theoretical Physics · University of Cambridge, UK

  8. Measuring Distortion in the Empty Regions of Dimensionality Reduction Scatterplots with the Gap Index

    Jul 30, 2026Jaume Ros, Alessio Arleo, Fernando PaulovichData VisualizationVisual Analytics

    Eindhoven University of Technology

  9. On a joint simultaneous learning of relevant feature subsets and subspaces in regression-like problems

    Jul 30, 2026Illia HorenkoScientific MLFeature Selection

    Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.

  10. FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction

    Jul 29, 2026Lucas Greff Meneses, Evandro S. Ortigossa, Claudio Silva +1Feature AttributionInverse Dimensionality Reduction

    University of São Paulo · Weizmann Institute of Science · New York University

  11. FloDR: An invertible dimensionality reduction method based on a normalising flow

    Jul 28, 2026Abdallah Baraka, Daniel ProbstData VisualizationVisual Analytics

    Bioinformatics Group Wageningen University & Research Wageningen 6708PB, The Netherlands

  12. A Riemannian View on Active Subspaces

    Jul 28, 2026Zachary GreyDimensionality ReductionRiemannian Geometry

  13. The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows

    Jul 27, 2026Alberto Solera-Rico, Patricia García-Caspueñas, Carlos Sanmiguel Vila +1Variational AutoencodersLatent Dynamics Modeling

    Sub-directorate general of aeronautical systems, Spanish National Institute for Aerospace Technology (INTA), ctra. M-301, km. 10.5, 28330 San Mart´ın de la Vega, Madrid, Spain. · Departamento de Ingenier´ıa Aeroespacial, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan´es, Madrid, Spain. · Department of Mechanical Engineering, University of Washington, 1410 NE Campus Parkway, Seattle, WA 98195, USA.

  14. Non--negative matrix factorization using the R package nnmf

    Jul 22, 2026Volkan Sevinç, Nikolas Kontemeniotis, Theodoros Perdikis +1Non-Negative Matrix FactorizationDimensionality Reduction

    Muğla Sıtkı Koçman University, Faculty of Science, Department of Statistics, Kötekli Kampüsü, Muğla, Türkiye · Department of Economics, University of Crete, Gallos Campus, Rethimno, Greece · Department of Tourism Studies, University of Piraeus, Piraeus, Greece +1

  15. A Bayesian Framework for Built-in Input Dimension Reduction for Gaussian Process Modeling

    Jul 21, 2026Eric Herrison Gyamfi, Emily L. Kang, Bledar A. Konomi +1Bayesian InferenceDeep Gaussian Processes

    Division of Statistics and Data Science, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH · Department of Mathematics, Purdue University, West Lafayette, IN

  16. Scaling Time Series Classification via XAI-Driven Data Reduction

    Jul 17, 2026Davide Italo Serramazza, Thach Le Nguyen, Georgiana IfrimExplainable Artificial IntelligenceTime Series Classification

    School of Computer Science, University College Dublin, Ireland

  17. Mathematics of Data Science

    Jul 11, 2026Afonso S. Bandeira, Amit Singer, Thomas StrohmerDimensionality Reduction

    ETH Zürich · Princeton University · UC Davis

  18. Terminal Dimension Reduction for Time Series with Applications

    Jul 10, 2026Alexander Munteanu, Matteo Russo, David Saulpic +1Coreset SelectionDimensionality Reduction

    TU Dortmund, Germany · EPFL, Switzerland · CNRS & Université Paris Cité, IRIF, Paris, France +1

  19. Group Invariant Spectral Embedding

    Jul 9, 2026Yeari Vigder, Paulina Hoyos, David Thong +3Manifold LearningDimensionality Reduction

    Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv, Israel · Department of Mathematics, University of Texas at Austin, Austin, TX, USA · Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden

  20. Dimensionality Reduction Meets Network Science: Sensemaking on UMAP's kNN Graph

    Jul 9, 2026Duen Horng Chau, Donghao Ren, Fred Hohman +1Dimensionality Reduction

    Apple

  21. Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spaces

    Jul 6, 2026Jeanie Schreiber, Tyrus Berry, Zeeshan AhmedRepresentation LearningPrincipal Component Analysis

    Department of Mathematical Sciences George Mason University Fairfax, VA 22030, USA · Sensor Science Division, Physical Measurement Laboratory NIST Gaithersburg, MD 20899, USA

  22. msPCA: An R Package for Sparse PCA with Multiple Components

    Jul 6, 2026Ryan Cory-Wright, Jean PauphiletPrincipal Component AnalysisDimensionality Reduction

    Analytics, Marketing and Operations Imperial Business School · Management Science and Operations London Business School

  23. Reduced-Order Models: The Mother of World Models

    Jul 3, 2026Rajat GhoshWorld ModelsAction-Conditioned World Models

    Independent Researcher

  24. Dimension Reduction for Curves: Simplified and Generalized

    Jul 3, 2026Matthijs Ebbens, Jie Lu, Alexander MunteanuDimensionality Reduction

    TU Dortmund, Germany

  25. Adjusted Wasserstein distances for bridging empirical and true distributions with applications to MDS

    Jun 29, 2026Flor Martinez-Sermeno, Arturo Jaramillo, Johan Van HorebeekMultidimensional ScalingDimensionality Reduction

  26. Autoencoder Architectures for Athlete Performance Scoring from Wearable Telemetry

    Jun 26, 2026Mateusz Kubita, Jan Zubalewicz, Krzysztof SiwekVariational AutoencodersAutoencoders

    Warsaw University of Technology Warsaw, Poland

  27. Graph Dimensionality Reduction for Contextual Bandits: Structure-Specific Regret Bounds under Approximate Smoothness and Noisy Eigenspaces

    Jun 26, 2026Joyanta Jyoti Mondal, Ibne Farabi Shihab, Anuj SharmaMulti-Armed BanditsGraph Bandits

    Department of Computer and Information Sciences, University of Delaware, USA · Department of Computer Science, Iowa State University, USA · Department of Civil, Construction & Environmental Engineering, Iowa State University, USA

  28. Dimensionality Reduction of QAOA Parameter Space with Kernel PCA for Max-Cut

    Jun 17, 2026Sidharth Brahmandam, Vayd RamkumarPrincipal Component AnalysisCombinatorial Optimization

    Naperville North High School · Independent Researcher

  29. Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance

    Jun 15, 2026Jernej Grlj, Aaron D. LaudaDimensionality ReductionSpectral Methods

    Department of Mathematics University of Southern California Los Angeles, CA 90089 · Department of Mathematics Department of Physics University of Southern California Los Angeles, CA 90089

  30. The Risk Shadow of Principal Component Analysis: When 99.9999% Variance Preservation Causes Catastrophic Decision Errors

    Jun 12, 2026Hamidou TembinePrincipal Component AnalysisDimensionality Reduction

    Department of EECS, School of Engineering, UQTR, Canada. Learning and Game Theory Laboratory (LnG Lab), TIMADIE.