Functional Data Analysis of Tree Data Objects.

نویسندگان

  • Dan Shen
  • Haipeng Shen
  • Shankar Bhamidi
  • Yolanda Muñoz Maldonado
  • Yongdai Kim
  • J S Marron
چکیده

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this paper is establishment of a connection between tree data spaces and the well developed area of Functional Data Analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length representation. These representations of trees in Euclidean spaces enable us to exploit the power of FDA to explore statistical properties of tree data objects. A major challenge in the analysis is the sparsity of tree branches in a sample of trees. We overcome this issue by using a tree pruning technique that focuses the analysis on important underlying population structures. This method parallels scale-space analysis in the sense that it reveals statistical properties of tree structured data over a range of scales. The effectiveness of these new approaches is demonstrated by some novel results obtained in the analysis of brain artery trees. The scale space analysis reveals a deeper relationship between structure and age. These methods are the first to find a statistically significant gender difference.

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عنوان ژورنال:
  • Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America

دوره 23 2  شماره 

صفحات  -

تاریخ انتشار 2014