In this paper we demonstrate the use of network analysis to characterise patterns of clustering in spatio-temporal events. Such clustering is of both theoretical and practical importance in the study of crime, and forms the basis for a number of preventative strategies. However, existing analytical methods show only that clustering is present in data, while offering little insight into the nature of the patterns present.
Here, we show how the classification of pairs of events as close in space and time can be used to define a network, thereby generalising previous approaches. The application of graph-theoretic techniques to these networks can then offer significantly deeper insight into the structure of the data than previously possible.
In particular, we focus on the identification of network motifs, which have clear interpretation in terms of spatio-temporal behaviour. Statistical analysis is complicated by the nature of the underlying data, and we provide a method by which appropriate randomised graphs can be generated. Two datasets are used as case studies: maritime piracy at the global scale, and residential burglary in an urban area.
In both cases, the same significant 3-vertex motif is found; this result suggests that incidents tend to occur not just in pairs, but in fact in larger groups within a restricted spatio-temporal domain. In the 4-vertex case, different motifs are found to be significant in each case, suggesting that this technique is capable of discriminating between clustering patterns at a finer granularity than previously possible.
Below: The mapping between event sets and their event networks. This schematic diagram represents the mapping between the space of event-sets and the space of event networks, for an illustrative case involving 4 events. For simplicity, the events are all assumed to be close temporal pairs, and the region is taken to be a square with width equal to the spatial close pair threshold. Only one configuration—that in which the events occur at the extremes of the region—maps to the empty network, whereas many possible event-sets map to the fully-connected network.
Full article at: http://goo.gl/Pa7Np3
- 1Department of Civil, Environmental and Geomatic Engineering, University College London, London, United Kingdom.
- 2Department of Security and Crime Science, University College London, London, United Kingdom.
- 3Centre for Advanced Spatial Analysis, University College London, London, United Kingdom.
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