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Activity Number:
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504
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Type:
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Topic Contributed
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Date/Time:
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Thursday, August 7, 2008 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #301248 |
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Title:
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Comparing Random Variables on Manifolds
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Author(s):
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Nikolay H. Balov*+
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Companies:
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Florida State University
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Address:
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117 N. Woodward Ave., Tallahassee, FL, 32306-4330,
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Keywords:
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covariance ; manifolds ; comparing distributions ; diffusion tensor imaging ; directional data ; similarity invariants
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Abstract:
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We are interested in comparing probability distributions defined on Riemannian manifolds. The traditional approach to study a distribution relies in locating the mean and finding the dispersion about that mean. On a general manifold however, even if two distributions are sufficiently concentrated and have unique means, a comparison of their covariances is not possible due to the difference in local parametrizations. To circumvent the problem we associate a covariance field with each distribution and compare them at common points by applying a similarity invariant function on their representing matrices. In this way we are able to define a distance between distributions. We discuss different choices of invariants and illustrate their properties through simulations. We also provide some results for studying Orientation Distribution Functions defined on unit sphere as appear in DTI analysis
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