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Exploring Spatial Patterns of Crime Using Non-hierarchical Cluster Analysis

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Book cover Crime Modeling and Mapping Using Geospatial Technologies

Part of the book series: Geotechnologies and the Environment ((GEOTECH,volume 8))

Abstract

Exploratory spatial data analysis (ESDA) is a useful approach for ­detecting patterns of criminal activity. ESDA includes a number of quantitative techniques and statistical methods that are helpful for identifying significant ­clusters of crime, commonly referred to as hot spots. Perhaps the most popular hot spot detection methods, both in research and practice, are based on tests of spatial autocorrelation and kernel density. Non-hierarchical clustering methods, such as k-means, are less used in many contexts. There is a perception that these approaches are less definitive. This chapter reviews non-hierarchical cluster analysis for crime hot spot detection. We detail alternative non-hierarchical approaches for spatial clustering that can incorporate both event attributes and neighborhood characteristics (i.e., spatial lag) as a modeling parameter. Analysis of violent crime in the city of Lima, Ohio is presented to illustrate this for hot spot detection. We conclude with a discussion of practical considerations in identifying hot spots.

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Notes

  1. 1.

    A discussion of hierarchical and non-hierarchical methods can be found in Hartigan (1975), Everitt (1993) and Kaufman and Rousseuw (2005), among others. Non-hierarchical, or partitioning, approaches identify a pre-specified number of clusters, k, such that each object is a member of exactly one cluster, where membership similarity is optimized. In contrast, hierarchical methods build clusters based on agglomeration (e.g., begin with n clusters and merge the two most similar groups to get n-1 clusters) or division (e.g., begin with one cluster and divide it into two most similar clusters), creating a decomposition hierarchy of clusters ranging from n to 1.

  2. 2.

    Lima, Ohio is a city of approximately 38,000 people and is located about 70 miles north of Dayton on the Interstate 75 corridor.

  3. 3.

    Details on multivariate integration for such purposes may be found in Kaufman and Rousseeuw (2005) as well as other clustering texts.

  4. 4.

    It is well known that any single application of the k-means heuristic is susceptible to becoming trapped in a local optima (Estivill-Castro and Murray 2000; Murray and Grubesic 2002), which prohibits the approach from identifying an optimal solution.

  5. 5.

    Analysis was carried out using 114 crime events in a neighborhood located in Akron, Ohio. The number of clusters obtained ranged from 4 to 11 (p  =  4–11). A separation value of 4 was utilized in the application of the k-means solution technique in CrimeStat for each value of p and the identified solution compared with the “optimal” solution using the approach reported in Murray and Grubesic (2002). For this range of clusters, the average sub-optimality of CrimeStat solutions was 38.28% (min  =  12.01%; max  =  72.19%). It should be noted that one can alter the separation distance in CrimeStat, in essence representing a pseudo-restart of the heuristic. Unfortunately, it is not possible to compare or assess cluster solution quality.

  6. 6.

    An assumed value of \( {f}_{i}=1\)implies the occurrence of a single event, rather than reflecting the aggregate summary of areas like police beats, census blocks or alternative areal units.

  7. 7.

    It is also common to view neighbors as being within a specified distance of a given location.

  8. 8.

    The legend in this case does not have the same interval interpretation as that shown in Figure 5.2. Rather than depicting interval ranges, only the median group value is shown. Once spatial lag importance is increased, it is unlikely that groups will have non-overlapping values characteristic of choropleth maps. This point is discussed in Murray and Shyy (2000).

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Acknowledgement

This material is based upon work supported by the National Science Foundation under grants SES-1154316 and SES-1154324. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Correspondence to Alan T. Murray .

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Murray, A.T., Grubesic, T.H. (2013). Exploring Spatial Patterns of Crime Using Non-hierarchical Cluster Analysis. In: Leitner, M. (eds) Crime Modeling and Mapping Using Geospatial Technologies. Geotechnologies and the Environment, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4997-9_5

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