论文标题
分解过滤的链复合物：金属编码算法后面的几何形状
Decomposing filtered chain complexes: geometry behind barcoding algorithms
论文作者
论文摘要
在拓扑数据分析中，过滤后的链复合物输入数据初始过滤和最终持久性不变式提取之间的持久管道。众所周知，他们承认一类不可分解的不可分解的人，称为间隔球。在本文中，我们提供了一种将过滤的链复合物分解为这样的间隔球的算法。该算法为标准持久性算法及其两个运行时优化的各个方面提供了几何见解。此外，由于它适用于任何过滤的链复合物，因此我们的算法可以在更一般的情况下应用。作为应用程序，我们展示了如何使用它分解过滤的内核。
In Topological Data Analysis, filtered chain complexes enter the persistence pipeline between the initial filtering of data and the final persistence invariants extraction. It is known that they admit a tame class of indecomposables, called interval spheres. In this paper, we provide an algorithm to decompose filtered chain complexes into such interval spheres. This algorithm provides geometric insights into various aspects of the standard persistence algorithm and two of its run-time optimizations. Moreover, since it works for any filtered chain complexes, our algorithm can be applied in more general cases. As an application, we show how to decompose filtered kernels with it.
