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A principal component analysis for trees. (English) Zbl 1184.62100
Summary: 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.

MSC:
62H25 Factor analysis and principal components; correspondence analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
05C90 Applications of graph theory
65C60 Computational problems in statistics (MSC2010)
Software:
fda (R)
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