In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in a systematic way by introducing bottleneck profiles. This leads to a notion of discrete Prokhorov metrics for persistence diagrams as a generalization of the Bottleneck distance. They satisfy a stability result and bounds with respect to Wasserstein metrics. We provide algorithms to compute the newly introduced quantities and end with an discussion about experiments.

翻译：在地形数据分析(TDA)中,持久性图是一个辅助工具。为了进行比较,通常使用瓦塞尔斯坦和博特勒内克距离。我们解决了这些指标的缺点,并通过引入瓶颈剖面,展示了系统调查的方法。这导致将持久性图的离散的Prokhorov 度量作为博特尔内克距离的概括概念。它们满足了瓦塞尔斯坦度量度的稳定性结果和界限。我们提供了计算新引进的数量的算法,并在实验结束时加以讨论。