交换、移动和修剪以折叠过滤
Swap, Shift and Trim to Edge Collapse a Filtration
摘要：
Boissonnat和Pritam引入了一种算法来减少对标记（或团）复合体的过滤，这特别可以加快其持久同源性的计算。他们使用所谓的边折叠来减少输入标志过滤，他们的减少方法只需要过滤的1-骨架。在本文中，我们重新使用的边折叠的持久性同源的有效计算。我们首先给出一个简单而直观的解释，该算法的基本原理。这反过来又使我们能够提出各种扩展，包括锯齿形过滤简化算法。最后，我们展示了一些实验来更好地理解它的行为。
英文摘要：
Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method required only the 1-skeleton of the filtration. In this paper we revisit the usage of edge collapse for efficient computation of persistence homology. We first give a simple and intuitive explanation of the principles underlying that algorithm. This in turn allows us to propose various extensions including a zigzag filtration simplification algorithm. We finally show some experiments to better understand how it behaves.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
