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.
Citation
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
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