This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 589
Type: Contributed
Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #306589
Title: High-Dimension, Low-Sample-Size Asymptotics Using Deterministic Geometric Structure of Stochastic Data: Application to an Extension of SVM for Data on Manifolds
Author(s): Suman Kumar Sen*+ and J. S. Marron and Mark Foskey and Sarang Joshi
Companies: Novartis Pharmaceuticals Corporation and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of Utah
Address: 25 Hickory Place, Apt K4, CHATHAM, NJ, 07928, USA
Keywords: manifold data ; support vector machine ; image analysis ; shape statistics ; HDLSS data ; statistical learning
Abstract:

In medical imaging and shape statistics, data are often times understood to be elements of a smooth manifold, and not the usual d-dimensional Euclidean space. A 'control point' based extension of SVM (called Manifold SVM) was recently developed which naturally handles such data. Such data are very challenging to visualize and we find a common underlying structure for a particular manifold by using a non-standard type of asymptotics: the dimension tends to infinity with fixed sample size. We show that pairwise distances on the manifold tend to be asymptotically a constant. These results are then used to show that the control point based extension of the Support Vector Machine asymptotically behaves like the extension of Mean Difference method, as dimension increases, paralleling previous Euclidean results. Few examples using m-rep(medial representation) of 3-dimensional images are shown.


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