The Jensen-Shannon divergence is a renown bounded symmetrization of the
unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler
divergence to the average mixture distribution. However the Jensen-Shannon
divergence between Gaussian distributions is not available in closed-form. To
bypass this problem, we present a generalization of the Jensen-Shannon (JS)
divergence using abstract means which yields closed-form expressions when the
mean is chosen according to the parametric family of distributions. More
generally, we define the JS-symmetrizations of any distance using generalized
statistical mixtures derived from abstract means. In particular, we first show
that the geometric mean is well-suited for exponential families, and report two
closed-form formula for (i) the geometric Jensen-Shannon divergence between
probability densities of the same exponential family, and (ii) the geometric
JS-symmetrization of the reverse Kullback-Leibler divergence. As a second
illustrating example, we show that the harmonic mean is well-suited for the
scale Cauchy distributions, and report a closed-form formula for the harmonic
Jensen-Shannon divergence between scale Cauchy distributions. We also define
generalized Jensen-Shannon divergences between matrices (e.g., quantum
Jensen-Shannon divergences) and consider clustering with respect to these novel
Jensen-Shannon divergences.

本文提出了一种使用抽象均值的 Jensen-Shannon（JS）差异的推广来绕过高斯分布之间的 JS 差异无法使用封闭形式表示的问题，并定义了任何距离的 JS 对称化。我们特别分别以几何平均和调和平均为例，推导了封闭形式的公式，其中包括基于相同指数族的概率密度之间的几何 JS 差异以及逆 Kullback-Leibler 差异的几何 JS 对称化，以及在剖面调和分布情况下的调和 JS 差异，同时定义了矩阵之间的 JS 差异，并考虑了在这些新型 JS 差异之下的聚类问题。