A Principal Component Analysis for Trees
Statistics Theory
2008-10-07 v2 Optimization and Control
Quantitative Methods
Computation
Statistics Theory
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 optimization problems. 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.
Keywords
Cite
@article{arxiv.0810.0944,
title = {A Principal Component Analysis for Trees},
author = {Burcu Aydin and Gabor Pataki and Haonan Wang and Elizabeth Bullitt and J. S. Marron},
journal= {arXiv preprint arXiv:0810.0944},
year = {2008}
}