Finding arbitrary shaped clusters with related extents in space and time

Abstract

The paper deals with density-based clustering of events, i.e. objects positioned in space and time, such as occurrences of earthquakes, forest fires, mobile phone calls, or photos taken by Flickr users. Finding concentrations of events in space and time can help to discover interesting places and time periods. The spatial and temporal properties of event clusters, in particular, their spatial and temporal extents and densities, can be related to each other. According to Tobler’s Law, the relationship can be described as follows. Events in a small area can be sparse in time and still connected. On the other hand, events in large areas are likely to be connected if they are close in time. Hence, the temporal distance threshold for density-based clustering should vary depending on the spatial extent of the area in which events happen. Therefore, we suggest a two-step clustering method. In the first step, spatial clusters of events are detected. In the second step, density-based clustering is applied to the temporal positions of spatially clustered events. The temporal distance threshold is chosen individually for each spatial cluster depending on its spatial extent. We demonstrate the work of the method on several examples of real data.