Introductory reading
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.[1]
One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: Computing persistent homology.[2]
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.[3]
Literature for Computer Scientists
A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: Computational topology: an introduction.[4]
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.[5]
The mapper algorithm. Singh et al: Topological methods for the analysis of high dimensional data sets and 3d object recognition.[6]
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.[7]
Literature for Biologists
References
- ↑ CARLSSON, Gunnar. Topology and data. Bulletin of the American Mathematical Society, 2009, 46. Jg., Nr. 2, S. 255-308. doi:10.1090/S0273-0979-09-01249-X
- ↑ ZOMORODIAN, Afra; CARLSSON, Gunnar. Computing persistent homology. Discrete & Computational Geometry, 2005, 33. Jg., Nr. 2, S. 249-274. doi:10.1007/s00454-004-1146-y
- ↑ BUBENIK, Peter. Statistical topological data analysis using persistence landscapes. The Journal of Machine Learning Research, 2015, 16. Jg., Nr. 1, S. 77-102. http://www.jmlr.org/papers/volume16/bubenik15a/bubenik15a.pdf
- ↑ EDELSBRUNNER, Herbert; HARER, John. Computational topology: an introduction. American Mathematical Soc., 2010.
- ↑ OTTER, Nina, et al. A roadmap for the computation of persistent homology. EPJ Data Science, 2017, 6. Jg., Nr. 1, S. 17. doi:10.1140/epjds/s13688-017-0109-5
- ↑ SINGH, Gurjeet; MÉMOLI, Facundo; CARLSSON, Gunnar E. Topological methods for the analysis of high dimensional data sets and 3d object recognition. In: SPBG. 2007. S. 91-100. doi:10.2312/SPBG/SPBG07/091-100
- ↑ 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