Object oriented data analysis: Sets of trees

Details Object oriented data analysis: Sets of trees Object oriented data analysis: Sets of trees

2007-11-20

arxiv.org/abs/0711.3147v1

Annals of Statistics 2007, Vol. 35, No. 5, 1849-1873

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000217 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000217

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.

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