Convergence of persistence diagrams for topological crackle
From MaRDI portal
Publication:2175001
DOI10.3150/20-BEJ1193zbMath1462.60070arXiv1810.01602MaRDI QIDQ2175001
Publication date: 27 April 2020
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.01602
Geometric probability and stochastic geometry (60D05) Persistent homology and applications, topological data analysis (55N31) Extreme value theory; extremal stochastic processes (60G70) Topological data analysis (62R40)
Related Items (4)
Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ Modelling persistence diagrams with planar point processes, and revealing topology with bagplots ⋮ Functional strong law of large numbers for Betti numbers in the tail
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Limit theorems for Betti numbers of random simplicial complexes
- Random geometric complexes in the thermodynamic regime
- Functional central limit theorem for subgraph counting processes
- Random geometric complexes
- The scaling limit of Poisson-driven order statistics with applications in geometric probability
- Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry
- Meta densities and the shape of their sample clouds
- A discussion on mean excess plots
- High risk scenarios and extremes. A geometric approach
- Topology of random geometric complexes: a survey
- Limit theorems for persistence diagrams
- Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes
- Maximally persistent cycles in random geometric complexes
- Weak limits for exploratory plots in the analysis of extremes
- Limit theorems for point processes under geometric constraints (and topological crackle)
- A functional non-central limit theorem for multiple-stable processes with long-range dependence
- Distance functions, critical points, and the topology of random Čech complexes
- Extremal theory for long range dependent infinitely divisible processes
- The topology of probability distributions on manifolds
- Finding the homology of submanifolds with high confidence from random samples
- Crackle: the homology of noise
- A Topological View of Unsupervised Learning from Noisy Data
- Topology and data
- Random Geometric Graphs
- QQ Plots, Random Sets and Data from a Heavy Tailed Distribution
- Theory of Random Sets
- Heavy-Tail Phenomena
- Barcodes: The persistent topology of data
This page was built for publication: Convergence of persistence diagrams for topological crackle
