Extending Hypothesis Testing with Persistence Homology to Three or More Groups
Methodology
2018-03-16 v1 Algebraic Topology
Abstract
We extend the work of Robinson and Turner to use hypothesis testing with persistence homology to test for measurable differences in shape between point clouds from three or more groups. Using samples of point clouds from three distinct groups, we conduct a large-scale simulation study to validate our proposed extension. We consider various combinations of groups, samples sizes and measurement errors in the simulation study, providing for each combination the percentage of -values below an alpha-level of 0.05. Additionally, we apply our method to a Cardiotocography data set and find statistically significant evidence of measurable differences in shape between normal, suspect and pathologic health status groups.
Cite
@article{arxiv.1602.03760,
title = {Extending Hypothesis Testing with Persistence Homology to Three or More Groups},
author = {Christopher Cericola and Inga Johnson and Joshua Kiers and Mitchell Krock and Jordan Purdy and Johanna Torrence},
journal= {arXiv preprint arXiv:1602.03760},
year = {2018}
}