Applications of the Voronoi Diagram by the Statistical Divergence

 

The Voronoi diagram is a fundamental discrete structure representing
the proximity of objects, and has been investigated in various ways.
Recently, Onishi and Imai have introduced the Voronoi diagram defined
by the statistical divergence, such as the Kullback-Leibler
divergence, for a set of probability distributions.  This Voronoi
diagram is a natural generalization of the Euclidean Voronoi diagram
and shares similar nice properties in term of convex polytopes and
hyperplane arrangements.


This talk discusses applications of this diagram to clustering
problems of texts and images in their feature space.  Also, the
Voronoi diagram defined by the mutual information is also
investigated.