Exploring geographic hotspots using topological data analysis

This article describes a scalar field topology (SFT)-based methodology for the interactive characterization and analysis of hotspots for density fields defined on a regular grid. In contrast to the common approach of simply identifying hotspots as areas that exceed a chosen density threshold, SFT provides various data abstractions—such as the merge tree and the Morse complex—to characterize hotspots and their boundaries at multiple scales. Moreover, SFT enables the ranking of hotspots based on analyst-defined importance measures, which also makes it possible to explore hotspots using a level-of-detail approach. We present a visual analytics system to support analysts in hotspot analysis and abstraction using SFT, and we demonstrate the merit of the proposed SFT-based methodology on two crime datasets.