This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. While this is helpful for data analysis using persistent homology, the results are sensitive to noise. In this paper, stable volumes and stable sub-volumes are proposed to solve this problem. For a special case, we prove that a stable volume is the robust part of an optimal volume against noise. We implemented stable volumes and sub-volumes on HomCloud, a data analysis software package based on persistent homology, and show examples of stable volumes and sub-volumes.

翻译：本文件提出了一个稳定的数量和稳定的量变量,称为稳定的子量,用于使用持久性同族体进行更可靠的数据分析。在以前的研究中,提出了最佳周期和类似的想法,以确定与持久性图中每一对生死对子相对应的同质结构。虽然这对使用持久性同质法进行数据分析很有帮助,但结果对噪音十分敏感。本文提出了稳定的数量和稳定的子量,以解决这个问题。对于一个特殊情况,我们证明稳定的量是防止噪音的最佳量的稳健部分。我们在HomCloud上采用了稳定的量和子量,这是基于持久性同质法的数据分析软件包,并展示了稳定的量和子量的实例。