Number of possible of Voronoi Partitions on the Feature Manifolds

概要

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In this paper, we analyze possible number of the k Voronoi partitions of n points on the feature manifold. In information geometry[1, 2, 8], differential geometric properties of probabilistic distribution have been studied. In the fields such as language recognition or learning theory, clustering of probability distributions, called"distributional clustering"minimizing sum of Kullback-Leibler divergence plays an important role. We take geometric approach for this distributional clustering problem and extend our result in the Euclidean space. We consider k-clustering problem of n distributions by divergence in general form on the manifold with dually flat property, and the generalized primary shatter functions for this Voronoi diagram is evaluated, which directly leads to a polynomial-time exact algorithm when the number of clusters and the dimension are regarded as constants.
一般社団法人情報処理学会の論文
2000-11-10