论文标题
MURIT：通过越过越过的越过越过的越过越过的标志复合物中路径持续条形码的有效计算
MuRiT: Efficient Computation of Pathwise Persistence Barcodes in Multi-Filtered Flag Complexes via Vietoris-Rips Transformations
论文作者
论文摘要
多参数持续的同源性自然出现在持续拓扑的应用中，这些数据取决于其他参数，例如时间序列数据。我们介绍了越野河流转换的概念，该方法可降低多滤波器旗复合物中路径子复合物的单参数持续的同源性，以计算越野河 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普斯 - 里普尔的越过某些半客户的同源性。相应的路径持久性条形码跟踪环境多过滤复合物的持久性特征，尤其可用于在多参数持续的同源性中恢复等级不变。我们提出MURIT，这是一种可扩展的算法，该算法通过越过越野河流转换来计算多过滤标志复合物的路径持续条形码。此外，我们提供了MURIT算法的有效软件实现，该软件依次诉诸vietoris-Rips持久性条形码的实际计算。为了证明MURIT对现实世界数据集的适用性，我们将MURIT建立为COVTREC管道的一部分，以监视当前Covid-19的大流行中冠状病毒SARS-COV-2的收敛进化。
Multi-parameter persistent homology naturally arises in applications of persistent topology to data that come with extra information depending on additional parameters, like for example time series data. We introduce the concept of a Vietoris-Rips transformation, a method that reduces the computation of the one-parameter persistent homology of pathwise subcomplexes in multi-filtered flag complexes to the computation of the Vietoris-Rips persistent homology of certain semimetric spaces. The corresponding pathwise persistence barcodes track persistence features of the ambient multi-filtered complex and can in particular be used to recover the rank invariant in multi-parameter persistent homology. We present MuRiT, a scalable algorithm that computes the pathwise persistence barcodes of multi-filtered flag complexes by means of Vietoris-Rips transformations. Moreover, we provide an efficient software implementation of the MuRiT algorithm which resorts to Ripser for the actual computation of Vietoris-Rips persistence barcodes. To demonstrate the applicability of MuRiT to real-world datasets, we establish MuRiT as part of our CoVtRec pipeline for the surveillance of the convergent evolution of the coronavirus SARS-CoV-2 in the current COVID-19 pandemic.
