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.
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.
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.
Details on multivariate integration for such purposes may be found in Kaufman and Rousseeuw (2005) as well as other clustering texts.
- 4.
- 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.
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.
It is also common to view neighbors as being within a specified distance of a given location.
- 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).
References
Aldenderfer M, Blashfield R (1984) Cluster analysis. Sage Publications, Beverly Hills
Anselin L (1995) Local indicators of spatial association-LISA. Geogr Anal 27:93–115
Anselin L (1998) Exploratory spatial data analysis in a geocomputational environment. In: Longley PA, Brooks SM, McDonnell R, Macmillan B (eds) Geocomputation, a primer. Wiley, New York
Anselin L, Cohen J, Cook D, Gorr W, Tita G (2000) Spatial analysis of crime. In: Criminal justice volume 4. Measurement and analysis of crime and justice. National Institute of Justice, Washington, DC
Anselin L, Syabri I, Kho Y (2006) Geoda: an introduction to spatial data analysis. Geogr Anal 38:5–22
Anselin L, Meyer WD, Whalley LA, Savoie MJ (2009) Actionable cultural understanding for support to tactical operations (ACUSTO). US army corps of engineers. ERDC/CERL TR-09-13
Anselin L, Rey SJ, Kochinsky J (2010) Flexible geospatial visual analytics and simulation technologies to enhance criminal justice decision support systems. Crime Mapp 3(1).
Armstrong MP, Xiao N, Bennett DA (2003) Using genetic algorithms to create multicriteria class intervals for Choropleth maps. Ann Assoc Am Geogr 93(3):595–623.
Arnold FJ (1979) A test for clusters. J Mark Res 16:545–551
Braga AA (2001) The effects of hot spots policing on crime. Ann Am Acad Polit Soc Sci 578(1):104–125
Brantingham PJ, Brantingham PL (1981) Environmental criminology. Waveland Press, Prospect Heights
Chainey S, Tompson L, Uhlig S (2008) The utility of hotspot mapping for predicting spatial patterns of crime. Secur J 21:4–28
Cohen LE, Felson M (1979) Social change and crime rate trends: a routine activity approach. Am Sociol Rev 44(4):588–608
Cohen MA, Rust RT, Steen S, Tidd ST (2004) Willingness-to-pay for crime control programs. Criminology 42(1):89–110
Cohon J (1978) Multiobjective programming and planning. Academic, New York
Cromley R (1995) Classed versus unclassed choropleth maps: a question of how many classes. Cartographic 32(4):15–27
Cromley RG, Cromley EK (2009) Choropleth map legend design for visualizing community health disparities. Int J Health Geogr 8:52
Dent B (1999) Cartography: thematic map design, 5th edn. WCB/McGraw-Hill, Boston
Eck JE, Chainey S, Cameron JG, Leitner M, Wilson RE (2005) Mapping crime: understanding hot spots. U.S. Department of Justice. https://www.ncjrs.gov/pdffiles1/nij/209393.pdf
Eck J, Liu L (2008) Varieties of artificial crime analysis: purpose, structure, and evidence in crime simulations. In: Liu L, Eck J (eds) Artificial crime analysis systems: using computer simulations and geographic information systems. Information Science Reference, Hershey, pp 413–432
Estivill-Castro V, Murray A (2000) Hybrid optimization for clustering in data mining. CLAIO 2000, on CD-ROM. IMSIO, Mexico
Everitt B (1993) Cluster analysis. Halsted, New York
Fisher W (1958) On grouping for maximum homogeneity. J Am Stat Assoc 53:789–798
Gordon AD (1996) How many clusters? An investigation of five procedures for detecting nested cluster structure. In: Hayashi C, Ohsumi N, Yajima K, Tanaka Y, Bock H, Baba Y (eds) Data science, classification, and related methods. Springer, Tokyo, pp 109–116
Gorr W, Olligschlaeger A, Thompson Y (2003) Short-term forecasting of crime. Int J Forecast 19(4):579–594
Griffith D, Amrhein C (1997) Multivariate statistical analysis for geographers. Prentice-Hall, Upper Saddle River
Grubesic TH (2006) On the application of fuzzy clustering for crime hot spot detection. J Quant Criminol 22(1):77–105
Grubesic TH, Mack EA (2008) Spatio-temporal interaction of urban crime. J Quant Criminol 24(3):285–306
Harries K (1999) Mapping crime: principle and practice. National Institute of Justice, Washington, DC
Hartigan J (1975) Clustering algorithms. Wiley, New York
Huang Z (1998) Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Min Knowl Discov 2:283–304.
Johnson SD, Bowers KJ (2004) The burglary as clue to the future: the beginnings of prospective hot-spotting. Eur J Criminol 1(2):237–255
Kaufman L, Rousseeuw PJ (2005) Finding groups in data. Wiley, New York.
Kent J, Leitner M (2007) Efficacy of standard deviational ellipses in the application of criminal geographic profiling. J Investig Psychol Offender Profil 4:147–165
LeBeau JL (1987) The methods and measures of centrography and the spatial dynamics of rape. J Quant Criminol 3:125–141
Leitner M, Barnett M, Kent J, Barnett T (2011) The impact of Hurricane Katrina on reported crimes in Louisiana: a spatial and temporal analysis. Prof Geogr 63(2):244–261
Levine N (2010) CrimeStat: A spatial statistics program for the analysis of crime incident locations, version 3.3. Ned Levine & Associates/National Institute of Justice, Washington, DC
Levine N (2006) Crime mapping and the crimestate program. Geogr Anal 38(1):41–56.
Lozano JA, Larranaga P, Grana M (1996) Partitional cluster analysis with genetic algorithms: searching for the number of clusters. In: Hayashi C, Ohsumi N, Yajima K, Tanaka Y, Bock H, Baba Y (eds) Data science, classification, and related methods. Springer, Tokyo, pp 117–124
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Le Cam L, Neyman J (eds) Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol I. University of California Press, Berkeley.
McLafferty S, Williamson D, McGuire PG (2000) Identifying crime hot spots using kernel smoothing. In: Goldsmith V, McGuire PG, Mollenkopf JH, Ross TA (eds) Analyzing crime patterns: frontiers of practice. Sage, Thousand Oaks, pp 77–85.
Messner SF, Anselin L, Baller RD, Hawkins DF, Deane J, Tolnay SE (1999) The spatial patterning of county homicide rates: an application of exploratory spatial data analysis. J Quant Criminol 15:423–450
Milligan GW, Cooper MC (1985) An examination of procedures for determining the number of clusters in a data set. Psychometrika 50:159–179
Milligan GW, Mahajan V (1980) A note on procedures for testing the quality of a clustering of a set of objects. Decis Sci 11:669–677
Morenoff JD, Sampson RJ, Raudenbush SW (2001) Neighborhood inequality, collective efficacy, and the spatial dynamics of urban violence. Criminology 39:517–559
Murray A (1999) Spatial analysis using clustering methods: evaluating the use of central point and median approaches. J Geogr Syst 1:367–383
Murray A (2000a) Spatial characteristics and comparisons of interaction and median clustering models. Geogr Anal 32:1–19
Murray A (2000b) Spatially lagged choropleth display. In: Forer P, Yeh A, He J (eds) In: Proceedings of 9th international symposium on spatial data handling, 1a40–49. International Geographical Union, Beijing
Murray A, Estivill-Castro V (1998) Cluster discovery techniques for exploratory spatial data analysis. Int J Geogr Inf Sci 12:431–443
Murray AT, Grubesic TH (2002) Identifying non-hierarchical spatial clusters. Int J Ind Eng 9:86–95.
Murray A, Shyy T (2000) Integrating attribute and space characteristics in choropleth display and spatial data mining. Int J Geogr Inf Sci 14:649–667
Murray A, McGuffog I, Western J, Mullins P (2001) Exploratory spatial data analysis techniques for examining urban crime. Br J Criminol 41:309–329
Openshaw S, Taylor P (1981) The modifiable areal unit problem. In: Wrigley N, Bennett R (eds) Quantitative geography: a British view. Routledge and Kegan Paul, London, pp 60–69
Parker RN (1985) Aggregation, ratio variables, and measurement problems in criminological research. J Quant Criminol 1:269–280
Podani J (1996) Explanatory variables in classifications and the detection of the optimum number of clusters. In: Hayashi C, Ohsumi N, Yajima K, Tanaka Y, Bock H, Baba Y (eds) Data science, classification, and related methods. Springer, Tokyo, pp 125–132
Ratcliffe JH (2002) Aoristic signatures and the spatio-temporal analysis of high volume crime patterns. J Quant Criminol 18(1):23–43
Ratcliffe JH (2004) The hotspot matrix: a framework for the spatio-temporal targeting of crime reduction. Police Pract Res 5(1):5–23
Ratcliffe JH (2005) Detecting spatial movement of intra-region crime patterns over time. J Quant Criminol 21(1):103–123
ReVelle C (1987) Urban public facility location. In: Mills E (ed) Handbook of regional and urban economics. Elsevier Science, New York
Rogerson P, Yamada I (2009) Statistical detection and surveillance of geographic clusters. CRC Press, New York
Rossmo DK (2000) Geographic profiling. CRC Press, Boca Raton
Rousseeuw P, Leroy A (1987) Robust regression and outlier detection. Wiley, New York
Sampson RJ, Groves WB (1989) Community structure and crime: testing social-disorganization theory. Am J Sociol 94:774–802
Shaw CR, McKay HD (1942) Juvenile delinquency and urban areas: a study of rates of delinquency in relation to differential characteristics of local communities in American cities. University of Chicago Press, Chicago
Shiode S, Shiode N (2009) Detection of multi-scale clusters in network space. Int J Geogr Inf Sci 23(1):75–92
Wang F (2005) Geographic information systems and crime analysis. Idea Group Publishing, Hershey
Wu X, Grubesic TH (2010) Identifying irregularly shaped crime hot-spots using a multiobjective evolutionary algorithm. J Geogr Syst 12:409–433
Xiao N, Armstrong MP (2005) ChoroWare: a software toolkit for Choropleth map classification. Geogr Anal 38(1):102–121.
Yamada I, Thill J-C (2007) Local indicators of network-constrained clusters in spatial point patterns. Geogr Anal 39(3):268–292.
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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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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