论文标题
迪拉克措施之间的hellinger-kantorovich barycenter
Hellinger-Kantorovich barycenter between Dirac measures
论文作者
论文摘要
Hellinger-Kantorovich（HK）距离是Wasserstein-2距离的不平衡延伸。最近表明，香港barycenter表现出比Wasserstein Barycenter的复杂行为。在这种观察过程中，我们更详细地研究了HK Barycenter，因为输入度量是无数的狄拉克度量集合，尤其是对HK的长度尺度参数的依赖性，而HK Barycenter是离散的还是连续的，以及预期的和经验的Barycenter之间的关系。分析结果与数值实验相辅相成，这些实验表明HK Barycenter可以提供输入点云或度量的粗到细节。
The Hellinger-Kantorovich (HK) distance is an unbalanced extension of the Wasserstein-2 distance. It was shown recently that the HK barycenter exhibits a much more complex behaviour than the Wasserstein barycenter. Motivated by this observation we study the HK barycenter in more detail for the case where the input measures are an uncountable collection of Dirac measures, in particular the dependency on the length scale parameter of HK, the question whether the HK barycenter is discrete or continuous and the relation between the expected and the empirical barycenter. The analytical results are complemented with numerical experiments that demonstrate that the HK barycenter can provide a coarse-to-fine representation of an input pointcloud or measure.
