Nielsen Frank
Sony Computer Science Laboratories, Tokyo 141-0022, Japan.
Entropy (Basel). 2020 Feb 16;22(2):221. doi: 10.3390/e22020221.
The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar α -Jensen-Bregman divergences and derive thereof the vector-skew α -Jensen-Shannon divergences. We prove that the vector-skew α -Jensen-Shannon divergences are -divergences and study the properties of these novel divergences. Finally, we report an iterative algorithm to numerically compute the Jensen-Shannon-type centroids for a set of probability densities belonging to a mixture family: This includes the case of the Jensen-Shannon centroid of a set of categorical distributions or normalized histograms.
詹森 - 香农散度是库尔贝克 - 莱布勒散度的一种著名的有界对称化形式，它不要求概率密度具有匹配的支撑集。在本文中，我们引入了标量α - 詹森 - 布雷格曼散度的向量偏斜推广，并由此推导出向量偏斜α - 詹森 - 香农散度。我们证明了向量偏斜α - 詹森 - 香农散度是 - 散度，并研究了这些新型散度的性质。最后，我们报告了一种迭代算法，用于数值计算属于混合族的一组概率密度的詹森 - 香农型质心：这包括一组分类分布或归一化直方图的詹森 - 香农质心的情况。
