Using Persistent Homology to Analyze Access to Heterogeneous-Quality Resources and Heterogeneous-Severity Nuisances

2026-09-28

AI Summary

This study addresses the analytical challenges in coverage assessment arising from the spatial heterogeneity of geographic resource quality and hazard severity by proposing a topological data analysis framework based on multiparameter persistent homology. Overcoming the limitations of conventional single-parameter approaches, this work designs a computationally efficient multiparameter approximation algorithm that enables quantitative evaluation of resource accessibility and hazard exposure under arbitrary quality criteria. Applied to a Chicago case study, the proposed method successfully identifies disparities in park accessibility as well as clusters of overexposure to facilities such as landfills and bars. By effectively capturing complex spatial dependencies, this framework establishes a new paradigm for assessing urban environmental equity.

Abstract

We develop a framework to use multiparameter persistent homology (PH) to examine access to heterogeneous-quality resources and exposure to heterogeneous-severity nuisances in a geographic region. Persistent homology, which is a type of topological data analysis {(TDA)}, has been employed previously to examine resource coverage. Unlike prior approaches, which used one-parameter PH to study resource coverage and nuisance exposure, our method accounts for heterogeneous-quality resources. Our framework, which employs a computationally-efficient approximation of multiparameter PH, allows one to study access to any resource ({or} exposure of any nuisance) using any notion of quality (or severity). Using the city of Chicago as an example region, we employ our framework to detect clusters of poor access to public parks, overexposure to landfills, and both underexposure and overexposure to pubs and bars.

Problem

• Persistent Homology
• Resource Access
• Nuisance Exposure
• Topological Data Analysis
• Heterogeneous Quality

Innovation

• Multiparameter Persistent Homology
• Topological Data Analysis
• Heterogeneous-Quality Resources
• Computational Approximation
• Spatial Accessibility