mlsanityData to 14 Oct 2026

A persistence landscapes toolbox for topological statistics

arXiv 1501.00179 ↗First posted 31 Dec 2014cs.CG cs.MS math.ATcited by 16

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Abstract (arXiv)

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning. We give efficient algorithms for calculating persistence landscapes, their averages, and distances between such averages. We discuss an implementation of these algorithms and some related procedures. These are intended to facilitate the combination of statistics and machine learning with topological data analysis. We present an experiment showing that the low-dimensional persistence landscapes of points sampled from spheres (and boxes) of varying dimensions differ.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Dec 2014.

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Citing papers per year: 2021: 1; 2022: 3; 2023: 4; 2024: 2; 2025: 2; 2026: 4.

16 papers.

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  1. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  2. 2022On the effectiveness of persistent homologycited by 20
  3. 2024Mapping the Multiverse of Latent Representationscited by 5
  4. 2023Landslide Topology Uncovers Failure Movementscited by 3
  5. 2021A Topological Data Analysis Based Classifiercited by 2
  6. 2025TACO-Net: Topological Signatures Triumph in 3D Object Classificationcited by 2
  7. 2022Transfer Learning for Autonomous Chatter Detection in Machiningcited by 1
  8. 2023A topological classifier to characterize brain states: When shape matters more than variancecited by 1
  9. 2024Novel definition and quantitative analysis of branch structure with topological data analysiscited by 1
  10. 2026Topological descriptors of foot clearance gait dynamics improve differential diagnosis of Parkinsonismcited by 1
  11. 2026From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Featurescited by 1
  12. 2026A Mathematical Framework for Topological Causal Data Analysiscited by 1
4 more
  1. 2022Individual Topology Structure of Eye Movement Trajectoriescited by 0
  2. 2023Machine learning and Topological data analysis identify unique features of human papillae in 3D scanscited by 0
  3. 2025Persistence Spheres: Bi-continuous Representations of Persistence Diagramscited by 0
  4. 2026Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagramscited by 0