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

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.