Work

Geometric Approaches to Persistent Homology

Year: 2022

Type: article

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.

Source: SIAM Journal on Applied Algebra and Geometry

DOI: 10.1137/21m1422914

Authors: Henry Adams, Baris Coskunuzer

Institutions: Colorado State University, The University of Texas at Dallas

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Award: DELTA: Descriptors of Energy Landscape by Topological Analysis