A PRINCIPAL COMPONENT ANALYSIS FOR TREES
A PRINCIPAL COMPONENT ANALYSIS FOR TREES
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DOI：
10.1214/09-aoas263
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发表时间：
2009-12-01
影响因子：
1.8
通讯作者：
Marron, J. S.
中科院分区：
文献类型：
--
作者：
Aydin, Burcu;Pataki, Gabor;Marron, J. S.
泛函数据分析的活跃领域(关于理解一组曲线中的变化)最近被扩展到面向对象的数据分析，它考虑了更一般的对象的总体。这一组思想的一个特别具有挑战性的扩展是树形结构对象的群体。我们基于树线的概念发展了一种类似于树的主成分分析，并提出了数值快速(线性时间)算法来解决所产生的问题，证明了其最优性。我们获得的解决方案被用于分析73个人的数据集，其中每个数据对象都是一个人大脑中的一棵血管树。我们的分析揭示了个体的年龄和他们的脑血管结构之间的显著关系。
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.