标题： 热带坐标在持久条形码空间上的应用 显示英文标题

标题： Tropical Coordinates on the Space of Persistence Barcodes

摘要： 应用拓扑学的目的是利用和发展拓扑方法应用于数学、科学和工程。其中一个主要工具是持久同调，它是经典同调的一个适应版本，它为一个有限度量空间分配一个条形码，即一系列区间。由于不变量的性质，条形码并不适用于机器学习任务中的从业者。我们可以通过为条形码分配数值来绕过这个问题，这些输出可以作为标准算法的输入。本文的目的是识别条形码空间上的热带坐标，并证明它们相对于瓶颈距离和Wasserstein距离是稳定的。 显示英文摘要

摘要： The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e. a collection of intervals, to a finite metric space. Because of the nature of the invariant, barcodes are not well-adapted for use by practitioners in machine learning tasks. We can circumvent this problem by assigning numerical quantities to barcodes and these outputs can then be used as input to standard algorithms. It is the purpose of this paper to identify tropical coordinates on the space of barcodes and prove that they are stable with respect to the bottleneck distance and Wasserstein distances.