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