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.
This research is partially supported by the Defense Advanced Research Projects Agency (DARPA), under grants HR0011-05-1-0057 and HR0011-09-0065, as well as the National Science Foundation (NSF), under grant DBI-0820624.
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Bendich, P., Edelsbrunner, H., Kerber, M., Patel, A. (2010). Persistent Homology under Non-uniform Error. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_2
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DOI: https://doi.org/10.1007/978-3-642-15155-2_2
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