带护送概率的对偶平坦结构及其在alpha-Voronoi图中的应用
Dually flat structure with escort probability and its application to alpha-Voronoi diagrams
摘要：
本文研究了护航概率分布流形的几何结构，并展示了它在情报学中的新应用。为了实现护送概率，我们使用了保角变换，它是离散概率分布空间的所谓α几何，它很好地表征了空间上的非加性统计。作为结果，护送概率被证明是平坦的坐标的通常概率导出的对偶平坦结构。最后，我们证明了护送概率与新的结构承认一个简单的算法来计算Voronoi图和质心相对于α发散。
英文摘要：
This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which well characterizes nonadditive statistics on the space. As a result escort probabilities are proved to be flat coordinates of the usual probabilities for the derived dually flat structure. Finally, we demonstrate that escort probabilities with the new structure admits a simple algorithm to compute Voronoi diagrams and centroids with respect to alpha-divergences.
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