mlsanityData to 7 Oct 2026

Stochastic Convergence of Persistence Landscapes and Silhouettes

arXiv 1312.0308 ↗First posted 2 Dec 2013math.ST cs.CG math.ATcited by 43

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Abstract (arXiv)

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly to a random sample of diagrams. Instead, we can summarize the persistent homology with the persistence landscape, introduced by Bubenik, which converts a diagram into a well-behaved real-valued function. We investigate the statistical properties of landscapes, such as weak convergence of the average landscapes and convergence of the bootstrap. In addition, we introduce an alternate functional summary of persistent homology, which we call the silhouette, and derive an analogous statistical theory.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Dec 2013.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 6; 2023: 9; 2024: 6; 2025: 2; 2026: 15.

43 papers.

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  1. 2022RipsNet: a general architecture for fast and robust estimation of the persistent homology of point cloudscited by 20
  2. 2022ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discoverycited by 13
  3. 2023TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Modelscited by 13
  4. 2024Persistent Topological Features in Large Language Modelscited by 11
  5. 2023PHG-Net: Persistent Homology Guided Medical Image Classificationcited by 9
  6. 2022Approximating Persistent Homology for Large Datasetscited by 8
  7. 2021Learning Hyperbolic Representations of Topological Featurescited by 7
  8. 2021A Random Persistence Diagram Generatorcited by 6
  9. 2023Improving Self-supervised Molecular Representation Learning using Persistent Homologycited by 6
  10. 2024Diffeomorphic interpolation for efficient persistence-based topological optimizationcited by 6
  11. 2024Mapping the Multiverse of Latent Representationscited by 5
  12. 2022Rethinking Persistent Homology for Visual Recognitioncited by 4
31 more
  1. 2024EMP: Effective Multidimensional Persistence for Graph Representation Learningcited by 4
  2. 2026Topological Causal Effectscited by 3
  3. 2022Topological EEG Nonlinear Dynamics Analysis for Emotion Recognitioncited by 2
  4. 2022Do Neural Networks Trained with Topological Features Learn Different Internal Representations?cited by 2
  5. 2023Image Classification using Combination of Topological Features and Neural Networkscited by 2
  6. 2024Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistencecited by 2
  7. 2021Homological Time Series Analysis of Sensor Signals from Power Plantscited by 1
  8. 2023A topological classifier to characterize brain states: When shape matters more than variancecited by 1
  9. 2023Stability for Inference with Persistent Homology Rank Functionscited by 1
  10. 2023A Topological Machine Learning Pipeline for Classificationcited by 1
  11. 2023Topological data analysis of human vowels: Persistent homologies across representation spacescited by 1
  12. 2024Explaining the Power of Topological Data Analysis in Graph Machine Learningcited by 1
  13. 2025CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizationscited by 1
  14. 2026Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonismcited by 1
  15. 2026The Density of Cross-Persistence Diagrams and Its Applicationscited by 1
  16. 2026Fixation Sequences as Time Series: A Topological Approach to Dyslexia Detectioncited by 1
  17. 2026A Mathematical Framework for Topological Causal Data Analysiscited by 1
  18. 2026TopoFormer: Topology Meets Attention for Graph Learningcited by 1
  19. 2026Persistent Convolution: A Topological Framework for AI Alignment Testing and Semantic Space Characterizationcited by 1
  20. 2021Statistical embedding: Beyond principal componentscited by 0
  21. 2021From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's researchcited by 0
  22. 2023Alzheimer Disease Detection from Raman Spectroscopy of the Cerebrospinal Fluid via Topological Machine Learningcited by 0
  23. 2025Time Series Analysis of Spiking Neural Systems via Transfer Entropy and Directed Persistent Homologycited by 0
  24. 2026TopoFisher: Learning Topological Summary Statistics by Maximizing Fisher Informationcited by 0
  25. 2026Vector Space of Cyclescited by 0
  26. 2026Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performancecited by 0
  27. 2026Quantum-Inspired Contextual Learning for Sparse-Ring Fraud Detection in Dynamic Transaction Graphscited by 0
  28. 2026Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagramscited by 0
  29. 2026Semantic Alignment of AI Models: Concept Collapse, Checkpoint Dynamics, and Cross-Lingual Transfercited by 0
  30. 2026Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learningcited by 0
  31. 2026Persistent Cross Entropycited by 0