Lipschitz functions have L_p-stable persistence
Cohen Steiner D, Edelsbrunner H, Harer J, Mileyko Y. 2010. Lipschitz functions have L_p-stable persistence. Foundations of Computational Mathematics. 10(2), 127–139.
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Journal Article
| Published
Author
Cohen-Steiner, David;
Edelsbrunner, HerbertISTA 
;
Harer, John;
Mileyko, Yuriy
;
Harer, John;
Mileyko, YuriyAbstract
We prove two stability results for Lipschitz functions on triangulable, compact metric spaces and consider applications of both to problems in systems biology. Given two functions, the first result is formulated in terms of the Wasserstein distance between their persistence diagrams and the second in terms of their total persistence.
Publishing Year
Date Published
2010-01-28
Journal Title
Foundations of Computational Mathematics
Acknowledgement
This research is partially supported by the Defense Advanced Research Projects Agency (DARPA) under grants HR0011-05-1-0007 and HR0011-05-1-0057 and by CNRS under grant PICS-3416.
Volume
10
Issue
2
Page
127 - 139
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Cite this
Cohen Steiner D, Edelsbrunner H, Harer J, Mileyko Y. Lipschitz functions have L_p-stable persistence. Foundations of Computational Mathematics. 2010;10(2):127-139. doi:10.1007/s10208-010-9060-6
Cohen Steiner, D., Edelsbrunner, H., Harer, J., & Mileyko, Y. (2010). Lipschitz functions have L_p-stable persistence. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-010-9060-6
Cohen Steiner, David, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko. “Lipschitz Functions Have L_p-Stable Persistence.” Foundations of Computational Mathematics. Springer, 2010. https://doi.org/10.1007/s10208-010-9060-6.
D. Cohen Steiner, H. Edelsbrunner, J. Harer, and Y. Mileyko, “Lipschitz functions have L_p-stable persistence,” Foundations of Computational Mathematics, vol. 10, no. 2. Springer, pp. 127–139, 2010.
Cohen Steiner D, Edelsbrunner H, Harer J, Mileyko Y. 2010. Lipschitz functions have L_p-stable persistence. Foundations of Computational Mathematics. 10(2), 127–139.
Cohen Steiner, David, et al. “Lipschitz Functions Have L_p-Stable Persistence.” Foundations of Computational Mathematics, vol. 10, no. 2, Springer, 2010, pp. 127–39, doi:10.1007/s10208-010-9060-6.
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