AI 中文总结
该研究提出一种基于约化到零微分和主动枚举的新算法计算图的离散同调，可算出Greene球的第四同调群，且在高噪声非度量环境下，其计算速度优于Vietoris-Rips复形的单纯同调，更适合含噪数据集。
AI 中文摘要
我们开发了一种新算法，用于通过约化到零微分和主动枚举来计算图的（持续）离散同调。该算法可计算Greene球的第四同调群以及若干此前未知的群。我们还证明，在高噪声非度量环境下，持续离散同调的计算速度比Vietoris-Rips复形的单纯同调更快，因此是含噪数据集的更优选择。
英文摘要
We develop a new algorithm for computing (persistent) discrete homology of graphs using reduction to zero differentials and active enumeration. This allows us to compute the fourth homology group of the Greene sphere, along with several previously unknown groups. We also show that persistent discrete homology computes faster than simplicial homology of Vietoris-Rips complex in the high-noise non-metric settings, making it a better choice for noisy data sets.
Comments21 pages; comments welcome
