A framework for differential calculus on persistence barcodes
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Publication:2162119
DOI10.1007/s10208-021-09522-yOpenAlexW3160568733MaRDI QIDQ2162119
Ulrike Tillmann, Jacob Leygonie, Steve Y. Oudot
Publication date: 5 August 2022
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.00960
Persistent homology and applications, topological data analysis (55N31) Computational aspects of data analysis and big data (68T09) Topological data analysis (62R40)
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Cites Work
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- The observable structure of persistence modules
- Stability of persistence diagrams
- Lipschitz functions have \(L_{p}\)-stable persistence
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- Tropical coordinates on the space of persistence barcodes
- Computing persistent homology
- Learning algebraic varieties from samples
- Topological persistence and simplification
- Continuation of point clouds via persistence diagrams
- Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport
- Stochastic subgradient method converges on tame functions
- Induced Matchings and the Algebraic Stability of Persistence Barcodes
- The Structure and Stability of Persistence Modules
- Morse Theory. (AM-51)
- Kernel method for persistence diagrams via kernel embedding and weight factor
- Stochastic Convergence of Persistence Landscapes and Silhouettes
- Notes on Topological Stability
- Decomposition of pointwise finite-dimensional persistence modules
- Persistence Images: A Stable Vector Representation of Persistent Homology
- Statistical topological data analysis using persistence landscapes
- An invitation to Morse theory
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