Minimization of the probabilistic p-frame potential

作者：Ehler M^*; Okoudjou K A

来源：Journal of Statistical Planning and Inference, 2012, 142(3): 645-659.

DOI：10.1016/j.jspi.2011.09.001

• Frame potential
• Equiangular tight frames
• Probabilistic frames
• Directional statistics
• Statistical shape analysis

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.

• 出版日期2012-3