论文标题
在单个通过中计算具有各种系数字段的持续同源性
Computing Persistent Homology with Various Coefficient Fields in a Single Pass
论文作者
论文摘要
本文介绍了一种算法，以计算单个矩阵还原中各种系数场的过滤复合物的持续同源性。该算法对不同系数字段的图表中的不同持续同源特征的总数具有输出敏感性。该计算使我们能够在任何规模上推断拓扑空间的积分同源组的扭转系数的质量分隔线，从而提供了比单个系数领域中持久性更有用的拓扑描述。我们提供理论复杂性分析以及详细的实验结果。该代码是Gudhi软件库的一部分。
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent homological features in the diagrams for the different coefficient fields. This computation allows us to infer the prime divisors of the torsion coefficients of the integral homology groups of the topological space at any scale, hence furnishing a more informative description of topology than persistence in a single coefficient field. We provide theoretical complexity analysis as well as detailed experimental results. The code is part of the Gudhi software library.
