Difference between revisions of "Introductory reading"
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== Literature for Mathematicians == | == Literature for Mathematicians == | ||
| − | A well-known theoretical introduction to the field. Carlsson: ''Topology and Data''. | + | A well-known theoretical introduction to the field. Carlsson: ''Topology and Data''. |
| − | One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: ''Computing persistent homology''. | + | One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: ''Computing persistent homology''. |
| − | A recently introduced topological summary better suited than persistence diagrams to statistically analyze persistent homology, the persistence landscape. Bubenik: ''Statistical topological data analysis using persistence landscapes.'' | + | A recently introduced topological summary better suited than persistence diagrams to statistically analyze persistent homology, the persistence landscape. Bubenik: ''Statistical topological data analysis using persistence landscapes.'' |
== Literature for Computer Scientists == | == Literature for Computer Scientists == | ||
| − | A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: ''Computational topology: an introduction'' | + | A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: ''Computational topology: an introduction''. |
| − | + | A general overview of persistent homology with an eye towards applications of different numerical libraries. In the supplementaries starting points for own numerical steps are given. Otter et al: ''A roadmap for the computation of persistent homology''. | |
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| − | + | The mapper algorithm. Singh et al: ''Topological methods for the analysis of high dimensional data sets and 3d object recognition.'' | |
| − | + | == Literature for Physicists == | |
| − | + | Starting with a topological primer, the computational setup is described and applied to immensely large structures present in our universe: the cosmic web. Pranav et al: ''The Topology of the Cosmic Web in Terms of Persistent Betti Numbers''.<ref>PRANAV, Pratyush, et al. The topology of the cosmic web in terms of persistent Betti numbers. ''Monthly Notices of the Royal Astronomical Society'', 2016, 465. Jg., Nr. 4, S. 4281-4310. [https://doi.org/10.1093/mnras/stw2862 doi:10.1093/mnras/stw2862]</ref> | |
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== Literature for Biologists == | == Literature for Biologists == | ||
== References == | == References == | ||
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Revision as of 21:00, 5 May 2019
This is a list of entries to the vastly growing literature in the field of topological data analysis, both from a theoretical and an applied point of view.
Literature for Mathematicians
A well-known theoretical introduction to the field. Carlsson: Topology and Data.
One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: Computing persistent homology.
A recently introduced topological summary better suited than persistence diagrams to statistically analyze persistent homology, the persistence landscape. Bubenik: Statistical topological data analysis using persistence landscapes.
Literature for Computer Scientists
A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: Computational topology: an introduction.
A general overview of persistent homology with an eye towards applications of different numerical libraries. In the supplementaries starting points for own numerical steps are given. Otter et al: A roadmap for the computation of persistent homology.
The mapper algorithm. Singh et al: Topological methods for the analysis of high dimensional data sets and 3d object recognition.
Literature for Physicists
Starting with a topological primer, the computational setup is described and applied to immensely large structures present in our universe: the cosmic web. Pranav et al: The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.[1]
Literature for Biologists
References
- ↑ PRANAV, Pratyush, et al. The topology of the cosmic web in terms of persistent Betti numbers. Monthly Notices of the Royal Astronomical Society, 2016, 465. Jg., Nr. 4, S. 4281-4310. doi:10.1093/mnras/stw2862