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Overview of object oriented data analysis
Author(s) -
Marron J. Steve,
Alonso Andrés M.
Publication year - 2014
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201300072
Subject(s) - euclidean geometry , computer science , object (grammar) , variety (cybernetics) , multiple correspondence analysis , correspondence analysis , principal component analysis , data analysis , multidimensional analysis , statistical analysis , data mining , mathematics , theoretical computer science , data science , artificial intelligence , statistics , machine learning , geometry
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 a variety of Euclidean approaches, such as principal components analysis, have been very successful. Challenges in modern medical image analysis motivate the statistical analysis of populations of more complex data objects that 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. The notion of object oriented data analysis also impacts data analysis, through providing a framework for discussion of the many choices needed in many modern complex data analyses, especially in interdisciplinary contexts.