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.