Extrinsic Data Analysis on Sample Spaces with a Manifold Stratification
作者： Rabi N Bhattacharya , M Buibas , Ian L Dryden , Leif A Ellingson , David Groisser
DOI:
关键词: Stratification (mathematics) 、 Mathematical analysis 、 Calculus 、 Probability distribution 、 Embedding 、 Asymptotic distribution 、 Mathematics 、 Population mean 、 Gaussian
摘要: Given a random object on stratified space embedded in numerical space, often times the extrinsic sample means stick to stratum that is closest population mean of corresponding probability distribution ambient via this embedding. In case an open book, limiting supported possibly lower dimensional stratum, extrinsically Gaussian stratum. Applications classical single various types image data analysis, including medical imaging, are also given.
ru.nl参考文章(24)
Mark Goresky, Robert MacPherson, Stratified Morse theory ,(1988)
A. Munk, S. Huckemann, T. Hotz, Intrinsic shape analysis: Geodesic principal component analysis for Riemannian manifolds modulo Lie group actions. Discussion paper with rejoinder. Statistica Sinica. ,vol. 20, pp. 1- 100 ,(2010)
Olivier D. Faugeras, What can be seen in three dimensions with an uncalibrated stereo rig european conference on computer vision. pp. 563- 578 ,(1992) , 10.1007/3-540-55426-2_61
STEPHAN HUCKEMANN, Inference on 3D Procrustes Means: Tree Bole Growth, Rank Deficient Diffusion Tensors and Perturbation Models. Scandinavian Journal of Statistics. ,vol. 38, pp. 424- 446 ,(2011) , 10.1111/J.1467-9469.2010.00724.X
A. Munk, R. Paige, J. Pang, V. Patrangenaru, F. Ruymgaart, The one- and multi-sample problem for functional data with application to projective shape analysis Journal of Multivariate Analysis. ,vol. 99, pp. 815- 833 ,(2008) , 10.1016/J.JMVA.2007.04.007
Armin Schwartzman, Robert F. Dougherty, Jonathan E. Taylor, False Discovery Rate Analysis of Brain Diffusion Direction Maps The Annals of Applied Statistics. ,vol. 2, pp. 153- 175 ,(2008) , 10.1214/07-AOAS133
Nicholas I. Fisher, Peter Hall, Bing-Yi Jing, Andrew T. A. Wood, Improved pivotal methods for constructing confidence regions with directional data Journal of the American Statistical Association. ,vol. 91, pp. 1062- 1070 ,(1996) , 10.1080/01621459.1996.10476976
Harrie Hendriks, Zinoviy Landsman, Mean Location and Sample Mean Location on Manifolds Journal of Multivariate Analysis. ,vol. 67, pp. 227- 243 ,(1998) , 10.1006/JMVA.1998.1776
Louis J. Billera, Karen Vogtmann, Susan P. Holmes, Geometry of the space of phylogenetic trees ,(2000)
Ian L Dryden, Alfred Kume, Huiling Le, Andrew TA Wood, A multi-dimensional scaling approach to shape analysis Biometrika. ,vol. 95, pp. 779- 798 ,(2008) , 10.1093/BIOMET/ASN050