Persistent homology—a survey

2008/01/01 by Herbert Edelsbrunner, John Harer · 6 citations
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Homology (biology) #Computational biology #Evolutionary biology #Biology #Genetics #Gene

paper · doi:10.1090/conm/453/08802

openalex publication_date 2008/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical formalism. Here we give a record of the short history of persistent homology and present its basic concepts. Besides the mathematics we focus on algorithms and mention the various connections to applications, including to biomolecules, biological networks, data analysis, and geometric modeling.

Cited by

• One-dimensional reduction of multidimensional persistent homology
• Visualizing High-Dimensional Data: Advances in the Past Decade
• Gromov‐Hausdorff Stable Signatures for Shapes using Persistence
• Persistent Homology of Collaboration Networks
• Geometry in the space of persistence modules
• Topological data analysis [wikipedia]