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Abstract Details
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Activity Number:
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549
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Type:
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Invited
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Date/Time:
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Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Statistical and Applied Mathematical Sciences Institute
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| Abstract - #300191 |
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Title:
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Manifold Data Analysis
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Author(s):
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Ian L. Dryden*+
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Companies:
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University of South Carolina
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Address:
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Department of Statistics, Columbia, SC, 29208,
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Keywords:
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Shape ;
Manifold ;
Geodesic ;
Principal components analysis ;
Sphere ;
Metric
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Abstract:
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Data that lie in a curved manifold are increasingly encountered in many application areas, for example in medical image analysis and computer vision. Classical manifold examples include spheres and landmark shape spaces, but newer manifold applications include spaces of curves, surfaces, diffusion tensors, diffeomorphisms and tree structures. Even defining the notion of a mean in a manifold is often not straighforward, and so care must be taken with the development of statistical methodology. Analogies of principal components analysis, regression models and smoothing splines in manifolds are some of the topics of interest. Particular distinctions are made between mildly non-Euclidean data, where the differential geometric structure is available, and strongly non-Euclidean data, where singularities and other complications abound.
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