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We develop a method for analyzing spatial and spatiotemporal anomalies ingeospatial data using topological data analysis (TDA). To do this, we usepersistent homology (PH), which allows one to algorithmically detect geometricvoids in a data set and quantify the persistence of such voids. We construct anefficient filtered simplicial complex (FSC) such that the voids in our FSC arein one-to-one correspondence with the anomalies. Our approach goes beyondsimply identifying anomalies; it also encodes information about therelationships between anomalies. We use vineyards, which one can interpret astime-varying persistence diagrams (which are an approach for visualizing PH),to track how the locations of the anomalies change with time. We conduct twocase studies using spatially heterogeneous COVID-19 data. First, we examinevaccination rates in New York City by zip code at a single point in time.Second, we study a year-long data set of COVID-19 case rates in neighborhoodsof the city of Los Angeles.

Analysis of Spatial and Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data