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.

Latest papers

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

Bridging Multi-Valued Heuristics and Dimensionality Reduction in Multi-Objective Search
Jun 5, 2026Maya Wolff, Ariel Felner, Oren SalzmanDimensionality Reduction Multi-Objective Optimization
Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel · Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems
Jun 4, 2026Edward T. Stevenson, Eric T. Wolf, Mei Ting Mak +2Latent Variable Models Climate Emulation
University of Cambridge · University of Colorado Boulder · University of Oxford +1
Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram
Jun 4, 2026Athanasios ZerisTransformer Interpretability Proper Orthogonal Decomposition
Independent Researcher, Athens, Greece.
Anchor PCA
Jun 4, 2026Benedikt Seiter, Anya Fries, Julius von Kügelgen +1Unsupervised Learning Principal Component Analysis
ETH Zürich
Dimensionality Reduction for Cyberattack Classification: A Comparative Evaluation of PCA and Linear Predictive Coding
Jun 4, 2026Nelly Elsayed, Zag ElSayed, Navid AsadizanjaniPredictive Coding Principal Component Analysis
School of Information Technology University of Cincinnati Ohio, United States · Dept. of Electrical & Computer Engineering University of Florida Florida, United States
On Out-of-sample Embedding in UMAP
Jun 3, 2026Mohammad Tariqul Islam, Jason W. FleischerManifold Learning Dimensionality Reduction
Media Lab, Massachusetts Institute of Technology, Cambridge, MA · Electrical and Computer Engineering, Princeton University, Princeton, NJ
A Robust Optimization Approach to Sparse Principal Component Analysis
Jun 2, 2026David Vävinggren, Francis Bach, André M. H. Teixeira +2Principal Component Analysis Robust Optimization
Uppsala University, Sweden · PSL Research University / INRIA, France · Science for Life Laboratory, Sweden
When Is 0.1% Enough? Analyzing the Combined Effects of Dimensionality Reduction and Quantization on Text Embedding Compression
May 31, 2026Riku Kisako, Hayato Tsukagoshi, Ryohei SasanoEmbedding Compression Dimensionality Reduction
Graduate School of Informatics, Nagoya University
Riemannian Stochastic Optimization for Sufficient Dimension Reduction
May 29, 2026Thibault Pautrel, François PortierStochastic Optimization Riemannian Optimization
Laboratoire des Signaux et Systèmes (L2S), CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France · ENSAI, CREST, Bruz, France
IRIS: time-structured manifold projections
May 29, 2026Brian Ondov, Chia-Hsuan Chang, Weipeng Zhou +6Data Visualization Manifold Learning
Department of Biomedical Informatics and Data Science, Yale School of Medicine, 333 Cedar St, New Haven, 06510, CT, USA. · School of Information, University of Michigan, 500 S. State St, Ann Arbor, 48109, MI, USA.
ScaleMAP: Preserving Local Density and Neighborhood Structure in Low-Dimensional Embeddings
May 28, 2026Rajas Poorna, Marcus T. CiceroneData Visualization Manifold Learning
Georgia Institute of Technology · School of Chemical and Biomolecular Engineering Georgia Institute of Technology · School of Chemistry and Biochemistry Georgia Institute of Technology
Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
May 28, 2026Yueyang Wang, Xili Wang, Kejun Tang +3Bayesian Inverse Problems Dimensionality Reduction
School of Mathematical Sciences, Peking University · School of Sciences, Great Bay University · Department of Mathematics, Louisiana State University +1
Dimensionality Reduction for Robust Federated Learning: A Theoretical Analysis and Convergence Guarantee
May 27, 2026Shiyuan Zuo, Jiashuo Li, Rongfei Fan +2Federated Learning Aggregation Byzantine-Robust Federated Learning
Beijing Institute of Technology, Beijing, China · Xi’an Jiaotong University, Xi’an, China · The Chinese University of Hong Kong (Shenzhen), Shenzhen, China
Sparse POD Mode Selection and Manifold Dimensionality Reduction with Neural Networks
May 26, 2026Tomoki Koike, Prakash Mohan, Marc T. Henry de Frahan +2Manifold Learning Feature Selection
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA · Computational Science Center, National Laboratory of the Rockies (NLR), Golden, CO
Supervised Distributional Reduction via Optimal Transport and Dependence Maximization
May 26, 2026Sai-Aakash Ramesh, Archit Sood, Andrew Corbett +1Kernel Methods Dimensionality Reduction
digiLab, UK · University of Bristol, UK
Similarity-based representation factorization for revealing interpretable dimensions in representational data
May 26, 2026Florian P. Mahner, Ka Chun Lam, Francisco Pereira +1Representation Learning Neural Representation Geometry
Max Planck Institute for Human Cognitive and Brain Sciences · National Institute of Mental Health · Justus Liebig University Giessen +1
Optimizing Multidimensional Scaling in Gini Metric Spaces
May 24, 2026Cassandra Mussard, Stéphane MussardMultidimensional Scaling Dimensionality Reduction
CESBIO, Univ. Toulouse Toulouse, France · CHROME, Univ. Nˆımes UM6P, AIRESS Nˆımes, France
MEDAL: Manifold Embedding Distillation via Autoencoder Learning
May 22, 2026Irene Chang, Tarek M. Zikry, Genevera I. AllenAutoencoders Manifold Learning
Department of Statistics, Columbia University, New York, NY 10027 · School of Data and Information Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 · Irving Institute for Cancer Dynamics, Columbia University, New York, NY 10027 +1
Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions
May 22, 2026Willem Diepeveen, Deanna NeedellManifold Learning Dimensionality Reduction
Department of Mathematics University of California, Los Angeles Los Angeles, CA 90095, USA
When One Point Is Not Enough: Addressing Ambiguous Instances in Dimensionality Reduction by Splitting
May 22, 2026Diede P. M. van der Hoorn, Alessio Arleo, Fernando V. PaulovichData Visualization Dimensionality Reduction
Eindhoven University of Technology
Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension
May 22, 2026Hong Qian, Xiang Shu, Xiang Xia +5Intrinsic Dimensionality Bayesian Optimization
Shanghai Institute of AI for Education, and School of Computer Science and Technology, East China Normal University, Shanghai 200062, China · Ant Group, Hangzhou 310013, China · Nanjing University, Nanjing 210023, China
Supervised Latent Restructuring for Small-Data Quantum Learning in Plant Phenomics
May 19, 2026Alakananda Mitra, David H. Fleisher, Vangimalla Reddy +1Plant Phenotyping Representation Learning
Nebraska Water Center, IANR University of Nebraska–Lincoln Lincoln, NE 68588 · Adaptive Cropping Systems Laboratory USDA-ARS Beltsville, MD 20705 · Nebraska Water Center, DWFI University of Nebraska–Lincoln Lincoln, NE 68588
Euclidean Embedding of Data Using Local Distances
May 19, 2026Dimitris ArabadjisManifold Learning Dimensionality Reduction
Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi, Samos, PA 83200
Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting
May 16, 2026João Paulo Gois, Luis Gustavo Nonato3D Gaussian Splatting Manifold Learning
Universidade Federal do ABC (UFABC), Santo André, Brazil · Instituto de Ciências Matemáticas e de Computação (ICMC), Universidade de São Paulo (USP), São Carlos, Brazil
Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models
May 14, 2026Libin Zhu, Damek Davis, Dmitriy Drusvyatskiy +1Kernel Ridge Regression Representation Learning
Department of Mathematics, University of Washington, Seattle, WA 98195 · Wharton Department of Statistics and Data Science, University of Pennsylvania, Philadelphia, PA 19104, USA · Department of Mathematics, U. Washington, Seattle, WA 98195 +1
Beyond Explained Variance: A Cautionary Tale of PCA
May 13, 2026Gionni MarchettiData Visualization Principal Component Analysis
Barcelona, Spain
Color Constancy in Hyperspectral Imaging via Reduced Spectral Spaces
May 13, 2026G. Dofri Vidarsson, Liying Lu, Sabine SüsstrunkColor Constancy Hyperspectral Imaging
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
NOFE - Neural Operator Function Embedding
May 12, 2026Lars Uebbing, Harald L. Joakimsen, Siyan Chen +6Inverse Dimensionality Reduction Sheaf Neural Networks
1UiT The Arctic University of Norway · 2Norwegian Computing Center · University of South Brittany +1
A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design
May 12, 2026Andrea Serani, Giorgio Palma, Matteo DiezGeometric Representation Learning Dimensionality Reduction
National Research Council-Institute of Marine Engineering, Rome, Italy
FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling
May 12, 2026Hongmin LiUnsupervised Learning Nyström Method
School of Life Science and Technology, Institute of Science Tokyo · 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan 2Department of Computational Biology and Medical Sciences Graduate School of Frontier Sciences, The University of Tokyo

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Bridging Multi-Valued Heuristics and Dimensionality Reduction in Multi-Objective Search

Maya Wolff, Ariel Felner, Oren Salzman

Department of Computer Science, Technion – Israel Institute of Technology, Haifa, Israel · Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Dimensionality Reduction Multi-Objective Optimization

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Multi-objective shortest-path (MOSP) algorithms traditionally rely on single-valued heuristics (SVHs), which associate each state with a single admissible cost vector. While SVHs provide safe lower bounds, they fail to capture the trade-off structure of the Pareto frontier and often yield weak search guidance. Multi-valued heuristics (MVHs) address this limitation by mapping states to sets of cost estimates, enabling a richer approximation of possible trade-offs. Modern MOSP algorithms are highly dependent on dimensionality reduction (DR) techniques to efficiently perform dominance checks. However, integrating MVHs with DR introduces subtle correctness challenges. We show that naively combining DR with MVHs destroys the ordering invariants required for DR, leading to unsound and incomplete search. To address this issue, we develop the first theoretical frameworks for safely integrating MVHs with DR. First, we introduce

\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}

, a theoretical baseline that restores search correctness by enforcing heuristic consistency. Recognizing the practical limitations of this approach, we then introduce our primary contribution,

\text{L}\text{-}\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}

. This algorithm employs a "lazy," optimistic approach to DR, preserving exact correctness with only an admissible MVH by dynamically detecting and repairing local ordering violations. Across a range of benchmarks,

\text{L}\text{-}\text{NAMOA}^*{\text{dr}\text{-}\text{mvh}}

matches or improves over state-of-the-art MOSP algorithms, and achieves speedups of over 10x in instances where the additional guidance provided by the MVH translates into stronger pruning.