PERSISTENT HOMOLOGY ANALYSIS OF BRAIN ARTERY TREES

被引：161

作者：

Bendich, Paul ^{[1
]}

Marron, J. S. ^{[2
]}

Miller, Ezra ^{[1
]}

Pieloch, Alex ^{[1
]}

Skwerer, Sean ^{[3
]}

机构：

[1] Duke Univ, Dept Math, Durham, NC 27708 USA

[2] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA

[3] Yale Univ, Sch Publ Hlth, Dept Biostat, New Haven, CT 06510 USA

来源：

ANNALS OF APPLIED STATISTICS | 2016年 / 10卷 / 01期

基金：

美国国家科学基金会;

关键词：

Persistent homology; statistics; angiography; tree-structured data; topological data analysis; PHYLOGENETIC TREES; DIAGRAMS; SPACE;

D O I：

10.1214/15-AOAS886

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：198 / 218

页数：21

共 35 条

[1]

Adcock Aaron, 2013, ARXIV13040530

[2]

[Anonymous], ARXIV14060214

[3]

[Anonymous], 1999, IMA VOLUMES MATH ITS

[4] A PRINCIPAL COMPONENT ANALYSIS FOR TREES [J].