The Annals of Applied Statistics

A principal component analysis for trees

Burcu Aydın, Gábor Pataki, Haonan Wang, Elizabeth Bullitt, and J. S. Marron

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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.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 4 (2009), 1597-1615.

Dates
First available in Project Euclid: 1 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1267453955

Digital Object Identifier
doi:10.1214/09-AOAS263

Mathematical Reviews number (MathSciNet)
MR2752149

Zentralblatt MATH identifier
1184.62100

Keywords
Object oriented data analysis population structure principal component analysis tree-lines tree-structured objects

Citation

Aydın, Burcu; Pataki, Gábor; Wang, Haonan; Bullitt, Elizabeth; Marron, J. S. A principal component analysis for trees. Ann. Appl. Stat. 3 (2009), no. 4, 1597--1615. doi:10.1214/09-AOAS263. https://projecteuclid.org/euclid.aoas/1267453955


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