Probability measures on the space of persistence diagrams
Publication
, Journal Article
Mileyko, Y; Mukherjee, S; Harer, J
Published in: Inverse Problems
December 1, 2011
This paper shows that the space of persistence diagrams has properties that allow for the definition of probability measures which support expectations, variances, percentiles and conditional probabilities. This provides a theoretical basis for a statistical treatment of persistence diagrams, for example computing sample averages and sample variances of persistence diagrams. We first prove that the space of persistence diagrams with the Wasserstein metric is complete and separable. We then prove a simple criterion for compactness in this space. These facts allow us to show the existence of the standard statistical objects needed to extend the theory of topological persistence to a much larger set of applications. © 2011 IOP Publishing Ltd.
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Published In
Inverse Problems
DOI
EISSN
1361-6420
ISSN
0266-5611
Publication Date
December 1, 2011
Volume
27
Issue
12
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0105 Mathematical Physics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
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Mileyko, Y., Mukherjee, S., & Harer, J. (2011). Probability measures on the space of persistence diagrams. Inverse Problems, 27(12). https://doi.org/10.1088/0266-5611/27/12/124007
Mileyko, Y., S. Mukherjee, and J. Harer. “Probability measures on the space of persistence diagrams.” Inverse Problems 27, no. 12 (December 1, 2011). https://doi.org/10.1088/0266-5611/27/12/124007.
Mileyko Y, Mukherjee S, Harer J. Probability measures on the space of persistence diagrams. Inverse Problems. 2011 Dec 1;27(12).
Mileyko, Y., et al. “Probability measures on the space of persistence diagrams.” Inverse Problems, vol. 27, no. 12, Dec. 2011. Scopus, doi:10.1088/0266-5611/27/12/124007.
Mileyko Y, Mukherjee S, Harer J. Probability measures on the space of persistence diagrams. Inverse Problems. 2011 Dec 1;27(12).
Published In
Inverse Problems
DOI
EISSN
1361-6420
ISSN
0266-5611
Publication Date
December 1, 2011
Volume
27
Issue
12
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0105 Mathematical Physics
- 0102 Applied Mathematics
- 0101 Pure Mathematics