Topological Data Analysis

Also known as TDA

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4 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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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
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
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 14, 2026Guanqun Ma, David Lenz, Kaiyuan Tang +4Topological Data Analysis
University of Utah · The Ohio State University
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 RoduAI Alignment Cross-Modal 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 Outcome Prediction Topological Data Analysis
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 Topological Data Analysis
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 Persistent Homology
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
$p$ -adic Bi-Filtrations for Topological Machine Learning on Genomic Sequences
Jun 4, 2026Tirtharaj Dash, Gunja SachdevaGenomics Persistent Homology
Department of CS & IS, BITS Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India. · Department of Mathematics, BITS Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India.
Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables
Jun 3, 2026Titouan Le Breton, Karol Szustakowski, Marie PiraudPersistent Homology Topological Data Analysis
1Helmholtz AI, Helmholtz Munich, Neuherberg, Germany · 2École des Ponts ParisTech, ENS Paris-Saclay · Institute of AI for Health, Helmholtz Munich, Neuherberg, Germany
Topological Ignorability for Structural Causal Effects Beyond Means
May 31, 2026Usef FaghihiCausal Effect Estimation Causal Identifiability
∗Université du Québec à Trois-Rivières (UQTR).
Periodic Topological Deep Learning for Polymer Design and Discovery
May 26, 2026Yasharth Yadav, Tze Kwang Gerald Er, Atsushi Goto +1Materials Property Prediction Molecular Representation Learning
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371 · School of Chemistry, Chemical Engineering and Biotechnology (CCEB), Nanyang Technological University, Singapore 637371
Topological Signal Processing: An Application-Oriented Tutorial
May 18, 2026Flavia Petruso, Maria Giulia Preti, Dimitri Van De VilleTopological Data Analysis
ToMAToMP: Robust and Multi-Parameter Topological Clustering
May 14, 2026Ludo Andrianirina, Mathieu CarrièreClustering Persistent Homology
DataShape, Centre Inria d’Université Côte d’Azur, Sophia-Antipolis, France
scShapeBench: Discovering geometry from high dimensional scRNAseq data
May 12, 2026Andrew J Steindl, João Felipe Rocha, Brian Tshilengi Di Bassinga +13Single-Cell RNA Sequencing Topological Data Analysis
Yale University · Mila / Université de Montréal · Garvan Institute of Medical Research +2
Towards Scalable Persistence-Based Topological Optimization
May 9, 2026Abderrahim Bendahi, Alexandre Duplessis, Arnaud FickingerPersistent Homology Topological Data Analysis
ENS Ulm, PSL Paris, France · UC Berkeley Berkeley, CA, USA
No Triangulation Without Representation: Generalization in Topological Deep Learning
May 7, 2026Johannes S. Schmidt, Martin Carrasco, Ernst Röell +3Neural Network Generalization Graph Neural Networks
Dept. of Math. & Statistics University of Montréal Montréal, Canada · Dept. of Informatics University of Fribourg Fribourg, Switzerland
Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecasting
May 4, 2026Usef Faghihi, Amir SakiTime Series Forecasting Persistent Homology
Department of Mathematics and computer science · University of Quebec Trois Rivieres
Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks
May 1, 2026Jiawen Chen, Qi Shao, Zhiqiang Ge +2Neural Network Expressivity Topological Data Analysis
Jiangsu Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University, Nanjing 210096, China
Monitoring Neural Training with Topology: A Footprint-Predictable Collapse Index
Apr 28, 2026Alexander KalinowskiRepresentation Collapse Neural Representation Geometry
SUNY Empire
DiRe-RAPIDS: Topology-faithful dimensionality reduction at scale
Apr 28, 2026Alexander Kolpakov, Igor RivinData Visualization Manifold Learning
CSTEM, University of Austin, Austin, TX, USA · Department of Mathematics, Temple University, Philadelphia, PA, USA
FILTR: Extracting Topological Features from Pretrained 3D Models
Apr 24, 2026Louis Martinez, Maks OvsjanikovPoint Cloud Learning 3D Representation Learning
LIX, ´Ecole Polytechnique, IP Paris
Fixation Sequences as Time Series: A Topological Approach to Dyslexia Detection
Apr 23, 2026Marius Huber, David R. Reich, Lena A. JägerTime Series Classification Eye Tracking
Department of Computational Linguistics, University of Zürich, Switzerland
Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells
Apr 19, 2026Mattie Ji, Indradyumna Roy, Vikas GargGraph Neural Networks Graph Representation Learning
University of Pennsylvania · Aalto University · Indian Institute of Technology Bombay +1
Spectral Kernel Dynamics for Planetary Surface Graphs: Distinction Dynamics and Topological Conservation
Apr 17, 2026Jnaneshwar DasDynamical Systems Spectral Methods
School of Earth and Space Exploration, Arizona State University
Persistent Entropy as a Detector of Phase Transitions
Feb 8, 2026Marcos Gutierrez-del-Pozo, Eduardo Paluzo-Hidalgo, Matteo RuccoPhase Transitions Persistent Homology
Exact and Approximate Range Queries in Ball Mapper
Jan 4, 2026Jay-Anne Bulauan, John Rick ManzanaresApproximation Algorithms Topological Data Analysis
Independent Researcher · Dioscuri Centre in Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences International Environmental Doctoral School of the University of Silesia in Katowice
Finite Topological Space Filtrations: A Topological Framework for Data Analysis
Dec 29, 2025Selçuk KayacanClustering Persistent Homology
Bahçeşehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey
Topological data analysis using persistent discrete homology
Jun 17, 2025Chris Kapulkin, Nathan KershawNoise Robustness Persistent Homology
Topology-enhanced machine learning for speech signal processing
Nov 26, 2023Pingyao Feng, Qingrui Qu, Haiyu Zhang +4Interpretable ML Speech Processing
Department of Mathematics, Southern University of Science and Technology, Shenzhen, China. · Department of Mathematics, North Carolina State University, Raleigh, NC, USA. · School of Intelligence Science and Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen, China. +1

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Where Do Two Populations of Persistence Diagrams Differ? Calibrated Local Inference at a Fixed Budget

Pramita Bagchi, Edward Bae, Atish Mitra, Alexander D. Silberman+2

The George Washington University · Montana Technological University · University of Ljubljana

Two-Sample Testing Confidence Region Estimation Multiple Hypothesis Testing Topological Data Analysis

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Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study simultaneous inference for local mean contrasts when the number of available diagrams is fixed. They are differences in expected weighted feature mass within

\ell_\infty

neighborhoods at several centers and radii. We estimate these contrasts using additive landmark responses. A Gaussian multiplier bootstrap calibrates simultaneous confidence intervals while allowing unequal group covariances. The neighborhoods whose intervals exclude zero form a map with approximate family-wise error control, and selecting a subset of original intervals for display preserves their joint coverage guarantee. On the simultaneous coverage event, every reported neighborhood lies within twice its radius of the support of the mean-measure difference. A geometric result gives sufficient radius conditions for a displaced feature to produce a nonzero contrast. A comparison of sufficient detection thresholds quantifies the tradeoff between reducing the number of tested coordinates and reserving observations for an independent pilot. In simulations with 40 to 120 diagrams per class, the bands achieved 94%-98% simultaneous coverage under both the strict null and equal means with unequal covariances. In the latter setting, a permutation maximum and the pooled-t implementation of the two-stage persistence-image test of Moon and Lazar rejected in up to 32% and 26% of runs, respectively. In the fixed-budget simulations, spending a third of the observations on a pilot to choose landmarks or radii located changes less often than a prespecified grid at a single radius. On the MUTAG benchmark, the localized region concentrates on rings of fused-ring systems, an exploratory reading.

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