The Annals of Statistics

Object oriented data analysis: Sets of trees

Haonan Wang and J. S. Marron

Full-text: Open access

Abstract

Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie groups and symmetric spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics. This point is illustrated through the careful development of a novel mathematical framework for statistical analysis of populations of tree-structured objects.

Article information

Source
Ann. Statist. Volume 35, Number 5 (2007), 1849-1873.

Dates
First available in Project Euclid: 7 November 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1194461714

Digital Object Identifier
doi:10.1214/009053607000000217

Mathematical Reviews number (MathSciNet)
MR2363955

Zentralblatt MATH identifier
1126.62002

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62G99: None of the above, but in this section

Keywords
Functional data analysis nonlinear data space object oriented data analysis population of tree-structured objects principal component analysis

Citation

Wang, Haonan; Marron, J. S. Object oriented data analysis: Sets of trees. Ann. Statist. 35 (2007), no. 5, 1849--1873. doi:10.1214/009053607000000217. http://projecteuclid.org/euclid.aos/1194461714.


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