title: Persistent Homology Analysis of Brain Artery Trees.
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.
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Paul
authors.initials: P
authors.lastname: Bendich
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599, USA.
authors.forename: J S
authors.initials: JS
authors.lastname: Marron
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Ezra
authors.initials: E
authors.lastname: Miller
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Pieloch
authors.affiliation: Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut 06510, USA.
authors.forename: Sean
authors.initials: S
authors.lastname: Skwerer
keywords: Persistent homology; angiography; statistics; topological data analysis; tree-structured data