Geometric Approaches to Persistent Homology
Henry Adams, Barış Coşkunuzer · SIAM Journal on Applied Algebra and Geometry · 2022
Abstract. We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the “life span” or “persistence” of a homology class. As a case study, we analyze the power filtration on unweighted graphs and provide explicit bounds for the life spans of homology classes in persistence diagrams in all dimensions.