Topological Data Analysis

Also known as TDA

Topological Data Analysis studies features such as connected components, loops, and higher-dimensional holes, and how they persist as data are viewed across scales. Persistent homology, Mapper and Reeb graphs, Euler characteristic transforms, and higher-order Laplacians turn these structures into summaries for clustering, classification, time-series analysis, and scientific discovery. Current work improves filtrations, statistical comparisons, and faster computation, while integrating topological features with neural networks and other machine-learning models. A central challenge is ensuring that measured structure reflects meaningful topology rather than noise, sampling density, or representation choices, while preserving stability and scaling to large datasets.

Latest papers

67 papers6 papers in the last four weeks, up 20% on the four weeks before. 0.0% of all new papers.

Explainable Prediction of High-Speed Solar Wind Streams driven by Coronal Holes via Topological Data Analysis
Oct 26, 2026Francesco Marchetti, Sabrina Guastavino, Daniel CollinSolar Physics Spatiotemporal Forecasting
Dipartimento di Matematica “Tullio Levi-Civita”, University of Padova, Italy · Osservatorio Astrofisico di Torino, Istituto Nazionale di Astrofisica, Torino, Italy · Dipartimento di Matematica, University of Genova, Italy +2
Topology-Inspired Fine-Tuning for Wind-Field Super-Resolution
Oct 15, 2026Arjun Dadhwal, Brian SummaImage Super-Resolution Topological Data Analysis
Tulane University
GPU-Accelerated Computation of Persistent Homology for Topological Analysis of Image Data
Oct 7, 2026Fan Wang, Hubert Wagner, Rezaul Chowdhury +1Persistent Homology Topological Data Analysis
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794 USA · Department of Mathematics, University of Florida, Gainesville, FL 32611 USA · Department of Biomedical Informatics, Stony Brook University, Stony Brook, NY 11794 USA
Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget
Oct 6, 2026Pramita Bagchi, Edward Bae, Atish Mitra +3Two-Sample Testing Confidence Region Estimation
The George Washington University · Montana Technological University · University of Ljubljana
The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
Oct 4, 2026Mattéo Clémot, Julie Digne, Julien TiernyPersistent Homology Topological Data Analysis
Université Lyon 1 · CNRS, Université Lyon 1 · CNRS, Sorbonne Université
$Ψ$ -Resilience: Model-Free Feature Importance from 1D Topological Signals
Oct 1, 2026Fabian Galis, Darian Onchis, Pedro Real JuradoFeature Attribution Topological Data Analysis
West University of Timis,oara · University of Sevilla
Higher-Order Positional Encodings for Graph Representation Learning
Oct 1, 2026Caleb Stam, Aagrim Hoysal, Sanjukta KrishnagopalGraph Representation Learning Positional Encoding
University of California, Santa Barbara
Period Segmentation in Transition Network Analysis: A Topological Data Analysis Approach
Sep 25, 2026Hitoshi Inoue, Koichi YasutakeChange-Point Detection Educational Data Mining
Nakamura Gakuen University, Fukuoka, Japan · Hiroshima University, Hiroshima, Japan
LandscapeSHAP: Which Persistent Homology Class Gets the Credit?
Sep 25, 2026Nikola MilićevićShapley Value Attribution Topological Data Analysis
Topological Signal Processing With Unoriented Operators
Sep 21, 2026Andrea Cavallo, Varun Sarathchandran, Geert Leus +1Graph Signal Processing Spectral Methods
Delft University of Technology, Delft, Netherlands
Direct Topology Tracking in Continuous Implicit Models
Sep 10, 2026Guanqun Ma, David Lenz, Kaiyuan Tang +4Topological Data Analysis
University of Utah · The Ohio State University
TopoFuse: Topology-Aware Tri-Planar Fusion for 3D Cryo-Electron Tomography Segmentation
Aug 31, 2026Rohit Kumar Salla, Neelesh Gupta, Xingjian Li +1Topology-Preserving Image Segmentation Image Segmentation
Virginia Tech, Blacksburg, VA, USA · National Institute of Technology, Kurukshetra, India · Carnegie Mellon University, Pittsburgh, PA, USA
Exploring Dowker Homology for Sentence Similarity
Aug 24, 2026Marius Huber, Juri OpitzSemantic Textual Similarity Topological Data Analysis
Department of Computational Linguistics University of Zürich
Structured Learning on Mapper Representations
Aug 22, 2026George Babus, Farzana NasrinTopological Representation Learning Topological Data Analysis
Department of Mathematics, University of Tennessee, Knoxville, TN -37916, USA
Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning
Aug 15, 2026Mathilde Papillon, Guillermo Bernárdez, Álvaro Ballón Barreiro +4Topological Representation Learning Topological Data Analysis
University of California Santa Barbara · Sapienza Universitá di Roma · Arlequin AI
Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning
Aug 6, 2026Farzana NasrinRL for Generative Models Persistent Homology
Department of Mathematics, University of Tennessee, Knoxville, TN -37916, USA
Persistent Convolution: A Topological Framework for AI Alignment Testing and Semantic Space Characterization
Jul 31, 2026Tyler Ashoff, Jordan RoduKG Entity Alignment AI Alignment
Department of Statistics, University of Virginia. · Department of Statistics, University of Virginia
Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction
Jul 26, 2026Jake Schwaderer, Alexander Bastien, Omid Khormali +3Sports Analytics Sports Outcome Prediction
Department of Mathematics University of Evansville Evansville, Indiana 47722, USA.
Quantum Topological Data Encoding
Jul 15, 2026Adam Wesołowski, Dimitrios Thanos, Daniel Leykam +1Quantum Machine Learning Quantum Data Encoding
Royal Holloway University of London, Department of Computer Science, UK · Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Leiden, The Netherlands · Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore +1
Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress
Jul 10, 2026Arul Rhik Mazumder, Shreyan Ronit MazumderQuantitative Finance Variational Quantum Algorithms
Carnegie Mellon University Pittsburgh, PA, USA · Cambridge Rindge and Latin School Cambridge, MA, USA
Shape Over Intensity: Directional Topological Encoding for False Positive Reduction in Intracranial Aneurysm Detection
Jul 6, 2026Akshay Gokhale, Mansi DhamneFDR Control Medical Image Anomaly Detection
Computer Science and Engineering Sardar Patel Institute of Technology Mumbai, India · Computer Engineering Sardar Patel Institute of Technology Mumbai, India
TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging
Jun 29, 2026Guangyu Meng, Pengfei Gu, Xueyang Li +3Medical Image Analysis Persistent Homology
Dept. of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, USA · Dept. of Computer Science, The University of Texas Rio Grande Valley, Edinburg, TX, USA
Topology-Informed Neural Networks for Flood Detection in Optical and Synthetic Aperture Radar Imagery
Jun 24, 2026Sophia Li, Max Zhao, Raghu G. Raj +1Remote Sensing Image Understanding Disaster Response
aU.S. Naval Research Laboratory, Washington, DC, USA · bStanford University, Stanford, CA, USA
Collapsed Effective Operators for Higher-order Structures
Jun 22, 2026Maximilian Krahn, Lennart Bastian, Vikas Garg +2Graph Clustering Spectral Methods
Department of Computing, Imperial College London, London, UK · Chair of Health Informatics, Technical University of Munich, Germany · Munich Center for Machine Learning, Germany +2
Topological summaries of fingerprint ridge patterns carry identity information
Jun 20, 2026Chad M. Topaz, Niny Arcila-Maya, Elizabeth Munch +2Biometric Identification Fingerprint Identification
Williams College, Williamstown, MA 01267 · QSIDE Institute, Williamstown, MA 01267 · University of Colorado Boulder, Boulder, CO 80309 +3
Topological Data Analysis for High-Dimensional Dynamic Process Monitoring
Jun 18, 2026Angan Mukherjee, Tyler A. Soderstrom, Michael J. Kurtz +1Process Supervision Topological Representation Learning
Department of Chemical & Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, WI 53706, USA · ExxonMobil Technology and Engineering, 22777 Springwoods Village Pkwy, Spring, TX 77389, USA
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
Jun 10, 2026Juliette Murris, Bernadette Stolz, Karsten BorgwardtTwo-Sample Testing Persistent Homology
Department of Machine Learning and Systems Biology, Max Planck Institute of Biochemistry, Martinsried, Germany
Encoding the Euler Characteristic Transform
Jun 9, 2026Nello Blaser, Odin Hoff Gardaa, Lars M. Salbu +2Representation Learning Geometric Representation Learning
Department of Informatics, University of Bergen, Norway · Department of Informatics, University of Fribourg, Switzerland
MS-COOT: Comparing Morse-Smale Complexes with Co-Optimal Transport
Jun 6, 2026Guangyu Meng, Mingzhe Li, Erin Wolf ChambersOptimal Transport Topological Data Analysis
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana, United States
Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
Jun 4, 2026Yan Wang, Tianyang HuRepresentational Similarity Analysis Neural Representation Geometry
School of Data Science The Chinese University of Hong Kong, Shenzhen

Oct 26, 2026J/K move · Enter open · S save

Explainable Prediction of High-Speed Solar Wind Streams driven by Coronal Holes via Topological Data Analysis

Francesco Marchetti, Sabrina Guastavino, Daniel Collin

Dipartimento di Matematica “Tullio Levi-Civita”, University of Padova, Italy · Osservatorio Astrofisico di Torino, Istituto Nazionale di Astrofisica, Torino, Italy · Dipartimento di Matematica, University of Genova, Italy+2

Solar Physics Spatiotemporal Forecasting Explainable Artificial Intelligence Topological Data Analysis

Open paper AskPDF arXiv

High-speed solar wind streams (HSSs) originating from coronal holes (CHs) are an important driver of recurrent geomagnetic activity. Since HSSs are associated to coronal structures visible in extreme-ultraviolet observations, this provides a natural basis for forecasting several days in advance. In this work, we investigate whether the topology of coronal structures observed in extreme ultraviolet (EUV) images contains predictive information on the subsequent occurrence of CH-driven HSSs at Earth. To this end, we consider Topological Data Analysis (TDA), and in particular persistent homology, to classify EUV solar images according to the occurrence of HSSs at Earth four days later. The target is a binary classification of HSS occurrence at a four-day lead time, defined using an HSS interval catalog and solar wind speed thresholds. Several combinations of topological representations and classifiers are evaluated under a common cross-validation framework. The results indicate that the topology of EUV coronal structures alone contains predictive information on subsequent CH-driven HSS occurrence, despite the absence of explicit CH geometric descriptors in the model input. To investigate the origin of this predictive information, we develop a model-level explainability framework based on cross-validation-aggregated feature weights and spatial evidence maps. A fully traced example connects persistence diagrams and persistence-image features to the classifier output and to their spatial localization in the original EUV observation. The proposed framework provides a transparent and computationally lightweight approach for investigating the relationship between coronal topology and subsequent high-speed solar wind streams.