Minimization of the probabilistic p-frame potential |
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| Authors: | M. Ehler K.A. Okoudjou |
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| Affiliation: | a Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Biomathematics and Biometry, Ingolstädter Landstr. 1, 85764 Neuherberg, Germany
b University of Maryland, Department of Mathematics, Norbert Wiener Center, College Park, MD 20742, United States |
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| Abstract: | We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory. Furthermore, we consider similar optimal configurations in terms of random distributions of points on the sphere. In this probabilistic setting, we characterize these optimal distributions by means of special classes of probabilistic frames. Our work also indicates some connections between statistical shape analysis and frame theory. |
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| Keywords: | Frame potential Equiangular tight frames Probabilistic frames Directional statistics Statistical shape analysis |
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