Persistent Homology Analysis of Brain Artery Trees

Paul Bendich, James Marron, Ezra Miller, Alex Pieloch, Sean Skwerer

Abstract:

New representations of tree-structured data objects, using ideas from topological data analysis,
enable improved statistical analyses of a population of brain artery trees. A number of represen-
tations of each data tree arise from persistence diagrams that quantify branching and looping of
vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries
of the persistence diagrams, lead to heightened correlations with covariates such as age and sex,
relative to earlier analyses of this data set. The correlation with age continues to be significant
even after controlling for correlations from earlier significant summaries