Fast computation of persistent homology representatives with involuted persistent homology
Fast computation of persistent homology representatives with involuted persistent homology
复制标题
具有内卷持久同源性的持久同源代表的快速计算
作者：
Matija vCufar;Žiga Virk
持久上同调通常通过持久上同调来计算。虽然这通常显著地改善了运行时间，但它不利于同源代表的提取。所提到的代表是相应孔的几何表示，并且通常携带所需的信息。我们提出了一种利用上同调来提取持久同调表示的新方法。简而言之，我们首先计算持久上同调，并利用所获得的信息来显著改善直接持久上同调计算的运行时间。该算法应用于Rips滤波，计算持久同调表示的速度一般比标准方法快得多。
Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of homology representatives. The mentioned representatives are geometric manifestations of the corresponding holes and often carry desirable information. We propose a new method of extraction of persistent homology representatives using cohomology. In a nutshell, we first compute persistent cohomology and use the obtained information to significantly improve the running time of the direct persistent homology computations. This algorithm applied to Rips filtrations generally computes persistent homology representatives much faster than the standard methods.