关于对称的Kullback-Leibler Jeffreys质心
On the symmetrical Kullback-Leibler Jeffreys centroids
摘要：
由于词袋建模范式的成功，聚类直方图已成为现代信息处理的重要组成部分。聚类直方图可以使用著名的$k$ -均值质心算法来执行。从应用的角度来看，通常需要处理对称距离。在这封信中，我们考虑的Jeffreys分歧，对称的Kullback-Leibler分歧，并调查Jeffreys质心的计算。我们首先证明了杰弗里斯质心可以用朗伯$W$函数的正直方图解析表示。然后，我们将展示如何获得一个快速保证近似处理时，频率直方图。最后，我们总结了$k$ -均值直方图聚类的一些评论。
英文摘要：
Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be performed using the celebrated $k$-means centroid-based algorithm. From the viewpoint of applications, it is usually required to deal with symmetric distances. In this letter, we consider the Jeffreys divergence that symmetrizes the Kullback-Leibler divergence, and investigate the computation of Jeffreys centroids. We first prove that the Jeffreys centroid can be expressed analytically using the Lambert $W$ function for positive histograms. We then show how to obtain a fast guaranteed approximation when dealing with frequency histograms. Finally, we conclude with some remarks on the $k$-means histogram clustering.
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