The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications

DOI10.1080/10618600.2019.1573686OpenAlexW2963636759MaRDI QIDQ3391276

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Publication date: 28 March 2022

Published in: Journal of Computational and Graphical Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00630

zbMATH Keywords

clusteringconfidence regiontwo-sample testpersistent homologyfunctional boxplotglobal rank envelope

Mathematics Subject Classification ID

Statistics (62-XX)

Related Items (11)

Measuring human activity spaces from GPS data with density ranking and summary curves ⋮ Testing goodness of fit for point processes via topological data analysis ⋮ A new measure for the attitude to mobility of Italian students and graduates: a topological data analysis approach ⋮ Bayesian topological learning for classifying the structure of biological networks ⋮ ToFU: topology functional units for deep learning ⋮ Topological data analysis of noise: uniform unimodal distributions ⋮ Unnamed Item ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ A random persistence diagram generator ⋮ Supervised learning with indefinite topological Kernels ⋮ A Bayesian Framework for Persistent Homology

Uses Software

• R
• spatstat
• scatterplot3d
• GET

Cites Work

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• Confidence sets for persistence diagrams
• Multiple Monte Carlo testing, with applications in spatial point processes
• Quantifying repulsiveness of determinantal point processes
• Spatial variation. 2nd ed
• Weak convergence and empirical processes. With applications to statistics
• Principal component analysis of persistent homology rank functions with case studies of spatial point patterns, sphere packing and colloids
• Measuring shape with topology
• An Introduction to the Theory of Point Processes
• On the Concept of Depth for Functional Data
• Determinantal Point Process Models and Statistical Inference
• Global Envelope Tests for Spatial Processes
• Statistical topological data analysis using persistence landscapes

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