Evaluating Cooling-Center Coverage Using Persistent Homology of a Filtered Witness Complex

In light of the increase in frequency of extreme heat events, there is a critical need to develop tools to identify geographic locations that are at risk of heat-related mortality. This paper aims to identify locations by assessing holes in cooling-center coverage using persistent homology (PH), a method from topological data analysis (TDA). Persistent homology has shown promising results in identifying holes in coverage of specific resources. We adapt these methods using a witness complex construction to study the coverage of cooling centers. We test our approach on four locations (central Boston, MA; central Austin, TX; Portland, OR; and Miami, FL) and use death times, a measurement of the size and scale of the gap in coverage, to identify most at risk regions. For comparison, we implement a standard technique for studying the risk of heat-related mortality called a heat vulnerability index (HVI). The HVI is a numerical score calculated for a geographic area based on demographic information. PH and the HVI identify different locations as vulnerable, thus indicating a potential value of assessing vulnerability from multiple perspectives. By using the regions identified by both persistent homology and the HVI, we provide a more holistic understanding of coverage.