Abstract
PHAT is a C++ library for the computation of persistent homology by matrix reduction. We aim for a simple generic design that decouples algorithms from data structures without sacrificing efficiency or user-friendliness. This makes PHAT a versatile platform for experimenting with algorithmic ideas and comparing them to state of the art implementations.
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Bauer, U., Kerber, M., Reininghaus, J.: Clear and compress: Computing persistent homology in chunks. In: Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization, pp. 103–117. Springer (2014)
Chen, C., Kerber, M.: Persistent homology computation with a twist. In: 27th European Workshop on Computational Geometry (EuroCG), pp. 197–200 (2011)
de Silva, V., Morozov, D., Vejdemo-Johansson, M.: Dualities in persistent (co)homology. Inverse Problems 27(12), 124003+ (2011)
Edelsbrunner, H., Harer, J.: Persistent homology — a survey. In: Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, pp. 257–282 (2008)
Edelsbrunner, H., Harer, J.: Computational Topology. An Introduction. American Mathematical Society (2010)
Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete & Computational Geometry 28(4), 511–533 (2002)
Forman, R.: Morse theory for cell complexes. Advances in Mathematics 134(1), 90–145 (1998)
Günther, D., Reininghaus, J., Wagner, H., Hotz, I.: Efficient computation of 3D Morse –Smale complexes and persistent homology using discrete Morse theory. The Visual Computer 28(10), 959–969 (2012)
Kasten, J., Reininghaus, J., Reich, W., Scheuermann, G.: Toward the extraction of saddle periodic orbits. In: Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization, pp. 55–69. Springer (2014)
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Bauer, U., Kerber, M., Reininghaus, J., Wagner, H. (2014). PHAT – Persistent Homology Algorithms Toolbox. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_24
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DOI: https://doi.org/10.1007/978-3-662-44199-2_24
Publisher Name: Springer, Berlin, Heidelberg
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