Persistent homology under non-uniform error

Authors:
Paul Bendich;Herbert Edelsbrunner;Michael Kerber;Amit Patel
Affiliations:
Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina and Dept. Mathematics, Duke Univ. Durham, North Carolina;Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina and Dept. Mathematics, Duke Univ. Durham, North Carolina and Geomagi ...;Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina;Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina
Venue:
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Year:
2010

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Abstract

Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classes. Prior work has shown that the homology and robustness information can be read off the extended persistence diagram of the function. This paper extends these results to a non-uniform error model in which perturbations vary in their magnitude across the domain.