2007/10/01 by Haonan Wang, J. S. Marron · 2 citations
Computer Science · Mathematics · #AI in cancer detection #Artificial intelligence #Computer science #Correspondence analysis #Data mining #Data structure #Euclidean geometry #Geometry #Mathematics #Medical Image Segmentation Techniques #Morphological variations and asymmetry #Object (grammar) #Population #Principal component analysis #Statistics #Theoretical computer science #math.ST #msc:62G99 #msc:62H99 #stat.TH
paper · pdf · doi:10.1214/009053607000000217
published as Annals of Statistics 2007, Vol. 35, No. 5, 1849-1873 · Published in at http://dx.doi.org/10.1214/009053607000000217 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/10/01 · arxiv created 2007/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.