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Extending
hypothesis testing with persistent homology to three or more
groups
Christopher Cericola, Inga Johnson, Joshua Kiers, Mitchell Krock, Jordan Purdy and Johanna Torrence
Vol. 11 (2018), No. 1, 27–51
DOI: 10.2140/involve.2018.11.27
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Abstract |
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We extend the work of Robinson and Turner to use hypothesis testing with persistent homology to test for measurable differences in shape between the spaces of three or more groups. We conduct a large-scale simulation study to validate our proposed extension, considering various combinations of groups, sample sizes and measurement errors. For each such combination, the percentage of p-values below an -level of 0.05 is provided. Additionally, we apply our method to a cardiotocography data set and find statistically significant evidence of measurable differences in shape between the spaces corresponding to normal, suspect and pathologic health status groups. |
Keywords
persistent homology, permutation test
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Mathematical Subject Classification 2010
Primary: 55N35, 62H15
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Milestones
Received: 14 January 2016
Revised: 8 August 2016
Accepted: 20 September 2016
Published: 17 July 2017
Communicated by Kenneth S. Berenhaut
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Authors |
| Christopher Cericola | |
| Department of Mathematics Louisiana State University Baton Rouge, LA 70803 United States |
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| Inga Johnson | |
| Department of Mathematics Willamette University Salem, OR 97301 United States |
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| Joshua Kiers | |
| Department of Mathematics University of North Carolina at Chapel Hill Chapel Hill, NC 27599 United States |
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| Mitchell Krock | |
| Department of Applied
Mathematics University of Colorado Boulder, CO 80309 United States |
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| Jordan Purdy | |
| Department of Mathematics Willamette University Salem, OR 97301 United States |
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| Johanna Torrence | |
| Department of Computer Science University of Chicago Chicago, IL 60637 United States |
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