The Annals of Applied Statistics

Persistent homology analysis of brain artery trees

Paul Bendich, J. S. Marron, Ezra Miller, Alex Pieloch, and Sean Skwerer

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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 representations 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.

Article information

Ann. Appl. Stat. Volume 10, Number 1 (2016), 198-218.

Received: December 2014
Revised: September 2015
First available in Project Euclid: 25 March 2016

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Zentralblatt MATH identifier

Persistent homology statistics angiography tree-structured data topological data analysis


Bendich, Paul; Marron, J. S.; Miller, Ezra; Pieloch, Alex; Skwerer, Sean. Persistent homology analysis of brain artery trees. Ann. Appl. Stat. 10 (2016), no. 1, 198--218. doi:10.1214/15-AOAS886.

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Supplemental materials

  • Supplement to “Persistent homology analysis of brain artery trees”. This archive contains brain tree data, persistence diagrams and statistical analysis pipeline for the paper.