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Abstract Details
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Activity Number:
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605
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Type:
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Topic Contributed
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Date/Time:
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Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #303393 |
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Title:
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Optimization Algorithms for Data Sampled from Spaces with Manifold Stratification
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Author(s):
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Sean Skwerer*+
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Companies:
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The University of North Carolina at Chapel Hill
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Address:
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8209 Old Deer Trail, Raleigh, NC, 27615,
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Keywords:
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optimization ;
algorithm ;
stratified ;
manifold ;
object
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Abstract:
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It has come to light that diverse data objects, from brain imaging, phylogenetic studies and shape statistics, can all be thought of as sampled from spaces with manifold stratification. Metrics between complex data objects arise naturally from the geometry of spaces with manifold stratification. None of commonly used statistical methods, including maximum likelihood estimation, principal component analysis, and linear regression, have been adapted to data sampled from spaces with manifold stratification. Understanding optimization on spaces with manifold stratification is essential to adapting the aforementioned statistical methods. Major considerations are the curvature of the spaces, the convexity of the objective function, and the complexity of the certificate of optimality. Specific examples of applications and algorithms will be included.
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Authors who are presenting talks have a * after their name.
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