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Exploring Spatial Patterns of Crime Using Non-hierarchical Cluster Analysis Alan T. Murray and Tony H. Grubesic

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. Keywords Clustering • Hot spots • Spatial patterns

A.T. Murray (*) GeoDa Center for Geospatial Analysis and Computation, School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ 85287-5302, USA e-mail: [email protected] T.H. Grubesic Geographic Information Systems and Spatial Analysis Laboratory, College of Information Science and Technology, Drexel University, Philadelphia, PA 19104, USA e-mail: [email protected] M. Leitner (ed.), Crime Modeling and Mapping Using Geospatial Technologies, Geotechnologies and the Environment 8, DOI 10.1007/978-94-007-4997-9_5, © Springer Science+Business Media Dordrecht 2013

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A.T. Murray and T.H. Grubesic

Introduction

Cluster detection and hot spot mapping in criminology, geography and related socio-economic planning sciences has evolved significantly over the past decade (Eck et al. 2005; Chainey et al. 2008). While many of the most basic approaches remain popular, such as spatial autocorrelation, spatial ellipses, kernel density estimation and spatial scan statistics (Wang 2005; Eck et al. 2005; Kent and Leitner 2007; Chainey et al. 2008; Rogerson and Yamada 2009; Anselin et al. 2009), advanced approaches now include fuzzy clustering (Grubesic 2006), spatio-temporal modeling of crime (Ratcliffe 2002; Grubesic and Mack 2008; Leitner et al. 2011), geospatial visual analytics (Anselin and Kochinsky 2010), and agent-based simulation (Eck and Liu 2008). Further, the emergence of proactive policing, predictive hot spotting and crime forecasting strategies suggests a growing need for objective spatial pattern detection methods to establish a better understanding of the distributions and morphologies crime (Cohen et al. 2004; Gorr et al. 2003; Johnson and Bowers 2004; Wu and Grubesic 2010). Broadly defined, a crime hot spot represents a grouping of incidents that are spatially and/or tem