Stable volumes for persistent homology

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