Abstract
This paper provides new tools for analyzing spatio-temporal event networks. We build time series of directed event networks for a set of spatial distances, and based on scan-statistics, the spatial distance that generates the strongest change of event network connections is chosen. In addition, we propose an empirical random network event generator to detect significant motifs throughout time. This generator preserves the spatial configuration but randomizes the order of the occurrence of events. To prevent the large number of links from masking the count of motifs, we propose using standardized counts of motifs at each time slot. Our methodology is able to detect interaction radius in space, build time series of networks, and describe changes in its topology over time, by means of identification of different types of motifs that allows for the understanding of the spatio-temporal dynamics of the phenomena. We illustrate our methodology by analyzing thefts occurred in Medellín (Colombia) between the years 2003 and 2015.
Highlights
The analysis of spatio-temporal point patterns appears in many areas of research related to crime, earthquakes, ecology, epidemiology, among many others
We, following Landau and Fridman (1993), consider that it is important to analyze the dynamics of the networks, and choose one distance to relate events in the network so that it is suitable in practical resolutions and helpful for decision-makers (Cozens et al 2019)
We extend the idea of Davies and Marchione (2015) by building a time series of event networks based on a division of the whole period into several time slots and spatial distances
Summary
The analysis of spatio-temporal point patterns appears in many areas of research related to crime, earthquakes, ecology, epidemiology, among many others. Following the Knox-test idea (Grubesic and Mack 2008), they build networks by varying spatial and temporal radius, obtaining location similarities ties (Borgatti et al 2009) Their procedure allows to observe the spatio-temporal closeness and the form of crimes, namely motifs, and find patterns with a fixed approach. We, following Landau and Fridman (1993), consider that it is important to analyze the dynamics of the networks, and choose one distance to relate events in the network so that it is suitable in practical resolutions and helpful for decision-makers (Cozens et al 2019) In this context, all the literature above commented do consider networks that neither preserve the topology nor vary with time. The analysis of real data related to crime in Medellin is shown in “Real data analysis” section, and the paper ends with some concluding remarks in “Discussion and conclusions” section
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