Extending Hypothesis Testing with Persistence Homology to Three or More Groups

TL;DR

This paper extends hypothesis testing with persistence homology to compare three or more groups, validating the method through simulations and real data analysis to detect shape differences.

Contribution

It introduces a novel extension of persistence homology hypothesis testing for multiple groups and validates it via extensive simulations and real-world data application.

Findings

Significant shape differences among health status groups in Cardiotocography data

Method reliably detects differences in simulated scenarios

Extension broadens the applicability of persistence homology testing

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 $p$-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.