Dimensionality Reduction

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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.

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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.

Orthogonal Subspace Clustering: Enhancing High-Dimensional Data Analysis through Adaptive Dimensionality Reduction and Efficient Clustering
Mar 16, 2026Qing-Yuan Wen, Da-Qing ZhangClustering Dimensionality Reduction
School of Science, University of Science and Technology Liaoning, Anshan, Liaoning Province, 114051, PR China
An Interpretable and Stable Framework for Sparse Principal Component Analysis
Mar 14, 2026Ying Hu, Hu YangPrincipal Component Analysis Dimensionality Reduction
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China
Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systems
Mar 13, 2026Nicolò Botteghi, Silke Glas, Christoph BruneAutoencoders PDE Surrogate Modeling
1MOX Laboratory, Department of Mathematics, Politecnico di Milano, Milano, Italy · Department of Applied Mathematics, University of Twente, Enschede, Netherlands
Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives
Mar 13, 2026Matteo Giacomini, Pedro DíezSurrogate Modeling Reduced-Order Modeling
Laboratori de Càlcul Numeric (LaCàN), E.T.S. de Ingeniería de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya - BarcelonaTech (UPC), Barcelona, Spain. · Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain.
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
mlx-vis: GPU-Native Dimensionality Reduction on Apple Silicon
Mar 4, 2026Han XiaoDimensionality Reduction GPU Acceleration
Elastic
The Theory behind UMAP?
Mar 2, 2026David WegmannCategory Theory Dimensionality Reduction
University of Erlangen-Nuremberg
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
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
Incremental dimension reduction for efficient and accurate visual anomaly detection
Feb 27, 2026Teng-Yok LeeDimensionality Reduction Anomaly Detection
Information R&D Technology Center, Mitsubishi Electric Coporation
ML-driven detection and reduction of ballast information in multi-modal datasets
Feb 18, 2026Yaroslav SolovkoFeature Selection Dimensionality Reduction
Independent Researcher, Dublin, Ireland
Thin Keys, Full Values: Reducing KV Cache via Low-Dimensional Attention Selection
Feb 16, 2026Hengshuai Yao, Xing Chen, Ahmed Murtadha +1Memory-Efficient Attention KV-Cache Compression
Sapient Intelligence · Department of Computing Science, University of Alberta
Multi-dimensional Persistent Sheaf Laplacians for Image Analysis
Feb 16, 2026Xiang Xiang Wang, Guo-Wei WeiTopological Representation Learning Image Classification
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA. · Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, MI 48824, USA. · Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA.
WavePhaseNet: A DFT-Based Method for Constructing Semantic Conceptual Hierarchy Structures (SCHS)
Feb 16, 2026Kiyotaka Kasubuchi, Kazuo FukiyaHierarchical Representation Learning Dimensionality Reduction
[affiliation]
PCA of probability measures: Sparse and Dense sampling regimes
Feb 2, 2026Gachon Erell, Jérémie Bigot, Elsa CazellesPrincipal Component Analysis Dimensionality Reduction
Institut de Mathématiques de Bordeaux, Université de Bordeaux, CNRS (UMR 5251) · CNRS, IRIT (UMR 5505), Université de Toulouse
Graph Regularized PCA
Jan 15, 2026Antonio Briola, Marwin Schmidt, Fabio Caccioli +4Graph Signal Processing Principal Component Analysis
1Shell Information Technology Limited, London, SE1 7NA, UK · University College London, Department of Computer Science, London, WC1E 6EA, UK · 4Systemic Risk Centre, London School of Economics and Political Sciences, London, WC2A 2AE, UK +1
Verification of Unknown Dynamical Systems via Autoencoder Latent Space
Dec 15, 2025Robert Reed, Luca Laurenti, Morteza LahijanianFormal Verification State Abstraction
Dept. of Aerospace Engineering University of Colorado Boulder Boulder, Colorado, USA · Delft University of Technology Delft, Netherlands · AI4I, Turin, Italy
Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization
Oct 17, 2025Luo Long, Coralia Cartis, Paz Fink ShustinVariational Autoencoders Bayesian Optimization
Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford, OX2 6GG, United Kingdom.
DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy
Aug 16, 2025Frederik L. Dennig, Daniel A. KeimVariational Autoencoders Uncertainty Quantification
University of Konstanz
Beyond Correlation: Learning Supervised, Sample-Distinct, and Eigenimage-Interpretable Representations
Jul 22, 2025Mojtaba MoattariRepresentation Learning Dimensionality Reduction
Independent Researcher
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
Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction
May 10, 2025Michael W. Trosset, Kaiyi Tan, Minh Tang +1Multidimensional Scaling Kernel Methods
Department of Statistics, Indiana University. · Department of Statistics, North Carolina State University. · Department of Applied Mathematics & Statistics, Johns Hopkins University.
Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction
Jan 31, 2025Daniel Herrera-Esposito, Johannes BurgeInformation Geometry Dimensionality Reduction
Department of Psychology University of Pennsylvania
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
Analytical Standard Errors for Exploratory Factor Solutions
Nov 12, 2018Xingwei Hu, Caihong Hu, Cheng-Kuang WuUncertainty Quantification Dimensionality Reduction
International Monetary Fund, Washington, DC, 20431, USA · Zhangjiajie College, Zhangjiajie, Hunan, 427000, China · Zhejiang Industry and Trade Vocational College, Wenzhou, Zhejiang, 325700, China

Mar 16, 2026J/K move · Enter open · S save

Orthogonal Subspace Clustering: Enhancing High-Dimensional Data Analysis through Adaptive Dimensionality Reduction and Efficient Clustering

Qing-Yuan Wen, Da-Qing Zhang

School of Science, University of Science and Technology Liaoning, Anshan, Liaoning Province, 114051, PR China

Clustering Dimensionality Reduction

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This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in a statistical sense, whose form exactly matches the paradigm of Q-type factor analysis. This theorem lays a solid mathematical foundation for dimensionality reduction via matrix decomposition and factor analysis. Based on this theorem, we propose the OSC framework to address the "curse of dimensionality" -- a critical challenge that degrades clustering effectiveness due to sample sparsity and ineffective distance metrics. OSC integrates orthogonal subspace construction with classical clustering techniques, introducing a data-driven mechanism to select the subspace dimension based on cumulative variance contribution. This avoids manual selection biases while maximizing the retention of discriminative information. By projecting high-dimensional data into an uncorrelated, low-dimensional orthogonal subspace, OSC significantly improves clustering efficiency, robustness, and accuracy. Extensive experiments on various benchmark datasets demonstrate the effectiveness of OSC, with thorough analysis of evaluation metrics including Cluster Accuracy (ACC), Normalized Mutual Information (NMI), and Adjusted Rand Index (ARI) highlighting its advantages over existing methods.