Persistent Homology

Latest papers 46

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

A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification
May 4, 2026Sushovan Majhi, Atish Mitra, Žiga Virk +1Point Cloud Classification Classification
Data Science, George Washington University, USA · Department of Mathematical Sciences, Montana Technological University, USA · Faculty of Computer and Information Science, University of Ljubljana, Institute IMFM, Slovenia +1
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
A Persistent Homology Design Space for 3D Point Cloud Deep Learning
Apr 5, 2026Prachi Kudeshia, Jiju Poovvancheri, Amr Ghoneim +1Persistent Homology Topological Representation Learning
Saint Mary’s University, Halifax, Canada · Nanjing Forestry University, China
How much of persistent homology is topology? A quantitative decomposition for spin model phase transitions
Mar 30, 2026Matthew LoftusPersistent Homology Topological Data Analysis
Cedar Loop LLC, Washington, USA
Persistence diagrams of random matrices via Morse theory: universality and a new spectral diagnostic
Mar 29, 2026Matthew LoftusRandom Matrix Theory Persistent Homology
Cedar Loop LLC, Washington, USA
GraPHFormer: A Multimodal Graph Persistent Homology Transformer for the Analysis of Neuroscience Morphologies
Mar 21, 2026Uzair Shah, Marco Agus, Mahmoud Gamal +5Topological Representation Learning Multimodal Graph Learning
Hamad Bin Khalifa University, Qatar · University of Turin, Italy · Neuroscience Institute Cavalieri Ottolenghi, Italy +3
Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transport
Mar 16, 2026Matteo PegoraroTopological Representation Learning Persistent Homology
Institute of Computing, Faculty of Informatics, Università della Svizzera Italiana
Beyond Distance: Quantifying Point Cloud Dynamics with Persistent Homology and Dynamic Optimal Transport
Mar 15, 2026Yixin Wang, Ting Gao, Jinqiao DuanTopological Data Analysis Optimal Transport
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China · Center for Mathematical Science, Huazhong University of Science and Technology, Wuhan, China · Steklov-Wuhan Institute for Mathematical Exploration, Huazhong University of Science and Technology, China +2
Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability
Mar 15, 2026Amir Saki, Usef FaghihiCausal Effect Estimation Causal Identifiability
Université du Québec à Trois-Rivières (UQTR).
The Density of Cross-Persistence Diagrams and Its Applications
Mar 12, 2026Alexander Mironenko, Evgeny. Burnaev, Serguei BarannikovTopological Data Analysis Density Estimation
Skolkovo Institute of Science and Technology, Moscow 121205, Russia · AIRI, Moscow 123317, Russia · CNRS, IMJ, Paris University, Paris 75205, France
G-LoG Bi-filtration for Medical Image Classification
Feb 20, 2026Qingsong Wang, Jiaxing He, Bingzhe Hou +3Topological Data Analysis Medical Image Classification
Persistent Entropy as a Detector of Phase Transitions
Feb 8, 2026Marcos Gutierrez-del-Pozo, Eduardo Paluzo-Hidalgo, Matteo RuccoPhase Transitions Persistent Homology
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

May 4, 2026J/K move · Enter open · S save

A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification

Sushovan Majhi, Atish Mitra, Žiga Virk, Pramita Bagchi

Data Science, George Washington University, USA · Department of Mathematical Sciences, Montana Technological University, USA · Faculty of Computer and Information Science, University of Ljubljana, Institute IMFM, Slovenia+1

Point Cloud Classification Classification Graph Classification Persistent Homology Statistical Learning Theory

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We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration. The embedding sums Mitra-Virk single-point coordinate functions over a sparse landmark grid; the closed-form weight rule

w_k^2 \propto (d_{k+1}^2 - d_k^2)/R_k^2

maximizes the distortion slope in Mitra-Virk's affine certificate under

ν

-coherence. (i) An

O(kR/(Δ\sqrt{m_{\min}}))

margin bound, driven by class-mean separation

Δ

and embedding radius

R

, matched in the sample-starved regime

m \lesssim R/Δ

by a Le Cam minimax lower bound. (ii) The Mahalanobis margin under Ledoit-Wolf-shrunk covariance is the strongest closed-form ranker on a 64-descriptor chemical-graph pool (mean Spearman

ρ= +0.56

across 11 benchmarks, positive on 10 of 11); the isotropic surrogate

Δ/\sqrt{\ell}

admits a closed-form selection-consistency rate on the homogeneous protein/social pools. (iii) A training-time-decided certificate, with no per-prediction overhead, in three concrete radii (Pinelis, Gaussian plug-in, and variance-aware Pinelis-Bernstein). Empirically, PLACE is the strongest diagram-based method on Orbit5k and matches the strongest topology-based baseline within statistical noise on MUTAG and COX2; remaining gaps fall into two diagnosable regimes (descriptor blindness on NCI1/NCI109; pool-coverage limits elsewhere). The Pinelis-Bernstein radius fires on 8 of the 12 benchmarks; on MUTAG the empirical and population nearest-centroid rules agree on every one of 940 held-out test predictions, validating the certificate's mechanism.