## 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.

### Duke Scholars

##### Altmetric Attention Stats

##### Dimensions Citation Stats

## 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

APA

Chicago

ICMJE

MLA

NLM

Mileyko, Y., Mukherjee, S., & Harer, J. (2011). Probability measures on the space of persistence diagrams.

*Inverse Problems*,*27*(12). https://doi.org/10.1088/0266-5611/27/12/124007Mileyko, 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