Voronoi diagram in statistical parametric space by Kullback-Leibler divergence
Voronoi diagram in statistical parametric space by Kullback-Leibler divergence
复制标题
Kullback-Leibler 散度统计参数空间中的 Voronoi 图
DOI：
10.1145/262839.263084
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
H. Imai
中科院分区：
文献类型：
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作者：
Kensuke Onishi;H. Imai
Voronoi图一直是计算几何中的一个重要课题，广义Voronoi图理论在机器人学、VLSI CAD等领域有着广泛的应用，已制定的安排，达文波特Schinzel序列和较低的信封。本文基于信息几何（Amari [1]），提出了在统计参数空间中引入离散邻近结构的新研究方向，即用统计意义距离定义的Voronoi图，并通过揭示其与欧氏Voronoi图的关系，构造了正则正态分布的上半空间Voronoi图.本文研究了正态分布的统计参数空间，采用Kullback-Leibler散度作为距离生成Voronoi图。KullbackLeibler分歧是信息论中最基本的分歧（例如，见[3，5]），并从这个分歧与[6，7]中得到的图表的相似性被示出。由于相对简单，Kullback-Leibler散度允许我们计算一般正态分布的Voronoi图。在推导本文的界时，充分利用了线性化技术和下包络参数。Voronoi图的其他分歧的统计参数空间的概率分布的离散变量采取d值也触及。
Voronoi diagram has been a main theme in computational geometry, and the theory of generalized Voronoi diagrams for various applications in robotics, VLSI CAD, etc., has been developed in terms of arrangements, Davenport-Schinzel sequences and lower envelopes. In this paper, we propose a new direction of research towards introducing discrete proximity structures in statistical parametric spaces by Voronoi diagrams defined by statistically meaningful distance, partially based on information geometry (Amari [1]), and the Voronoi diagram in the upper half space is constructed for canonical normal distributions by revealing its relation with the Euclidean Voronoi diagram. This paper investigates the statistical parametric space of normal distributions by adopting the Kullback-Leibler divergence as a distance to generate the Voronoi diagram. The KullbackLeibler divergence is the most fundamental divergence in information theory (e.g., see [3, 5]), and similarity of the diagram obtained from this divergence with that in [6, 7] is shown. Due to relative simplicity, the Kullback-Leibler divergence allows us to compute the Voronoi diagram for general normal distribution. Linearization technique as well as lower envelope arguments is fully made use of in deriving bounds of this paper. Voronoi diagrams for other divergences in the statistical parametric space of probability distribution of a discrete variable taking d values are also touched upon.