Approximating continuous functions on persistence diagrams using template functions
From MaRDI portal
Publication:6047301
DOI10.1007/s10208-022-09567-7arXiv1902.07190OpenAlexW2917416770MaRDI QIDQ6047301
Elizabeth Munch, Jose A. Perea, Firas A. Khasawneh
Publication date: 7 September 2023
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.07190
Persistent homology and applications, topological data analysis (55N31) Learning and adaptive systems in artificial intelligence (68T05) Geometric embeddings of metric spaces (30L05)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Confidence sets for persistence diagrams
- Symmetric and \(r\)-symmetric tropical polynomials and rational functions
- The ring of algebraic functions on persistence bar codes
- Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
- On computing Poincaré map by Hénon method
- Fréchet means for distributions of persistence diagrams
- Stability of persistence diagrams
- On the numerical computation of Poincaré maps
- Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
- Tropical coordinates on the space of persistence barcodes
- Zigzag persistence
- Universality of persistence diagrams and the bottleneck and Wasserstein distances
- Functional summaries of persistence diagrams
- Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport
- Topological spaces of persistence modules and their properties
- Probabilistic Fréchet means for time varying persistence diagrams
- The theory of the interleaving distance on multidimensional persistence modules
- A new test for chaos in deterministic systems
- Probability measures on the space of persistence diagrams
- The Structure and Stability of Persistence Modules
- On the validity of the 0–1 test for chaos
- Ergodic theory of chaos and strange attractors
- Kernel method for persistence diagrams via kernel embedding and weight factor
- Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
- Stochastic Convergence of Persistence Landscapes and Silhouettes
- Barycentric Lagrange Interpolation
- Decomposition of pointwise finite-dimensional persistence modules
- Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
- Persistence Images: A Stable Vector Representation of Persistent Homology
- Sampling from a Manifold
- Statistical topological data analysis using persistence landscapes
