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March 2016 Persistent homology analysis of brain artery trees
Paul Bendich, J. S. Marron, Ezra Miller, Alex Pieloch, Sean Skwerer
Ann. Appl. Stat. 10(1): 198-218 (March 2016). DOI: 10.1214/15-AOAS886

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 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.

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Paul Bendich. J. S. Marron. Ezra Miller. Alex Pieloch. Sean Skwerer. "Persistent homology analysis of brain artery trees." Ann. Appl. Stat. 10 (1) 198 - 218, March 2016. https://doi.org/10.1214/15-AOAS886

Information

Received: 1 December 2014; Revised: 1 September 2015; Published: March 2016
First available in Project Euclid: 25 March 2016

MathSciNet: MR3480493
Digital Object Identifier: 10.1214/15-AOAS886

Keywords: angiography , Persistent homology , statistics , topological data analysis , tree-structured data

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.10 • No. 1 • March 2016
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