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December 2009 A principal component analysis for trees
Burcu Aydın, Gábor Pataki, Haonan Wang, Elizabeth Bullitt, J. S. Marron
Ann. Appl. Stat. 3(4): 1597-1615 (December 2009). DOI: 10.1214/09-AOAS263

Abstract

The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of tree-structured objects. We develop an analog of Principal Component Analysis for trees, based on the notion of tree-lines, and propose numerically fast (linear time) algorithms to solve the resulting problems to proven optimality. The solutions we obtain are used in the analysis of a data set of 73 individuals, where each data object is a tree of blood vessels in one person’s brain. Our analysis revealed a significant relation between the age of the individuals and their brain vessel structure.

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Burcu Aydın. Gábor Pataki. Haonan Wang. Elizabeth Bullitt. J. S. Marron. "A principal component analysis for trees." Ann. Appl. Stat. 3 (4) 1597 - 1615, December 2009. https://doi.org/10.1214/09-AOAS263

Information

Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1184.62100
MathSciNet: MR2752149
Digital Object Identifier: 10.1214/09-AOAS263

Keywords: Object oriented data analysis , population structure , Principal Component Analysis , tree-lines , tree-structured objects

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 4 • December 2009
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