Vol. 11, No. 1, 2018

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ISSN: 1944-4184 (e-only)
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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
Abstract

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 α-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
Mathematical Subject Classification 2010
Primary: 55N35, 62H15
Milestones
Received: 14 January 2016
Revised: 8 August 2016
Accepted: 20 September 2016
Published: 17 July 2017

Communicated by Kenneth S. Berenhaut
Authors
Christopher Cericola
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803
United States
Inga Johnson
Department of Mathematics
Willamette University
Salem, OR 97301
United States
Joshua Kiers
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599
United States
Mitchell Krock
Department of Applied Mathematics
University of Colorado
Boulder, CO 80309
United States
Jordan Purdy
Department of Mathematics
Willamette University
Salem, OR 97301
United States
Johanna Torrence
Department of Computer Science
University of Chicago
Chicago, IL 60637
United States