Abstract: We consider problems to classify data represented as discrete probability distributions. For the classification we propose the Voronoi partition technique with respect to -divergence, which is a statistically justified pseudo- distance on the space of probability distributions. In order to improve computational efficiency and performance of the classification, we introduce two nonlinear transformations respectively called the escort and projective transform, and weighted -centroids. Finally we demonstrate performances of the proposed tools via simple numerical examples.

Keywords: -divergence, -Voronoi partition, Escort transformation, Projective transformation

ACM Classification Keywords: I.3.5 Computational Geometry and Object Modeling

MSC: 53A15, 68T10

Link:

GEOMETRICAL TOOLS FOR ALPHA-VORONOI PARTITIONS

Atsumi Ohara and Yuya Nagatani

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p17.pdf