title: Overview of object oriented data analysis.
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 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.
authors.affiliation: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599, USA.
authors.forename: J Steve
authors.initials: JS
authors.lastname: Marron
authors.affiliation: Department of Statistics and INEACU, Universidad Carlos III de Madrid, Calle Madrid 126, 28903, Getafe, Spain.
authors.forename: Andrés M
authors.initials: AM
authors.lastname: Alonso
mesh_terms: D001699:Biometry; D003627:Data Interpretation, Statistical; D008954:Models, Biological; D025341:Principal Component Analysis; D013223:Statistics as Topic / Q000639:trends
keywords: Data objects; Functional data analysis; Non-Euclidean; Principal components