Crime

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Network-based space-time search-window technique for hotspotdetection of street-level crimeincidentsShino Shiode a & Narushige Shiode ba Department of Geography, Environment and DevelopmentStudies , Birkbeck College, University of London , London , UKb School of Planning and Geography , Cardiff University , Cardiff ,UKPublished online: 07 Nov 2012.

To cite this article: Shino Shiode & Narushige Shiode (2013) Network-based space-time search-window technique for hotspot detection of street-level crime incidents, International Journal ofGeographical Information Science, 27:5, 866-882, DOI: 10.1080/13658816.2012.724175

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International Journal of Geographical Information Science, 2013Vol. 27, No. 5, 866–882, http://dx.doi.org/10.1080/13658816.2012.724175

Network-based space-time search-window technique for hotspotdetection of street-level crime incidents

Shino Shiodea* and Narushige Shiodeb

aDepartment of Geography, Environment and Development Studies, Birkbeck College, University ofLondon, London, UK; bSchool of Planning and Geography, Cardiff University, Cardiff, UK

(Received 17 January 2012; final version received 20 August 2012)

This study proposes a street-level space-time hotspot detection method to analyse crimeincidents recorded at the street-address level and provides description of the micro-levelvariation of crime incidents over space and time. It expands the notion of search-win-dow techniques widely used in crime science by developing a method that can accountfor the spatial-temporal distribution of crime incidents measured in network distance.The study first describes the methodological framework by presenting the concept of anew type of search window and how it is used in the process of statistical testing fordetecting crime hotspots. This is followed by analyses using (1) a simulated distribu-tion of points along the street network, and (2) a set of real street-crime incident data.The simulation study demonstrates that the proposed method is effective in identify-ing space-time hotspots, which include those that are not detected by a non-temporalmethod. The empirical analysis of the drug markets and assaults in downtown Buffalo,New York, revealed a detailed space-time signature of each type of crime, highlight-ing the recurrent nature of drug dealing at specific locations as well as the sporadictendency of assault incidents.

Keywords: space-time hotspot; street address; network; search window

1. Introduction

Recent studies suggest that micro-scale approaches are establishing firm base within thefield of geography of crime (Taylor 1997, Weisburd et al. 2009a, 2009b, Braga andWeisburd 2010, Groff et al. 2010). Of the many topics on micro-scale approaches, detec-tion of crime hotspots, or significant concentrations of crime incidents, remains a focalresearch theme (Sherman and Weisburd 1995, Weisburd and Braga 2006). The enduringinterest in micro-scale crime hotspots exists primarily because the detected hotspots actas an important indicator for identifying high-risk locations that require further attentionand action, possibly through place-based intervention. Braga et al. (2010) point out that agrowing body of research suggests that hotspot policing focused on micro-places is effec-tive in reducing crime. In addition, Mazerolle et al. (2006), in their study of intervention bylaw enforcements on the street-level drug marketing, refer to problem-oriented policing asanother key geographically focused tactic for targeting micro-space hotspots. The develop-ment of these policing tactics is indicative of the fact that hotspot detection is considered tobe effective in providing police enforcements with more focused and efficient allocation of

*Corresponding author. Email: [email protected]

© 2013 Taylor & Francis

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mailto:[email protected]

International Journal of Geographical Information Science 867

their resources to combat crime (Weisburd et al. 2004, Groff et al. 2010). At the same time,literature has also shown that the distribution pattern, as well as the nature of hotspots,varies by the type of offence (Krivo and Peterson 1996, Kubrin and Herting 2003, Hipp2010, Bernasco and Block 2011). These differences have direct relevance to the policingtactics and, as such, make it vital to accurately identify for each specific type of crimethe exact locations of hotspots. The continued interest in micro-spatial hotspot detection isalso sustained by growing evidence of the presence of crime hotspots at micro-places orhighly localised places (Johnson et al. 2009, Weisburd et al. 2009b). Empirical findingsindeed confirm the tendency for crime incidents to concentrate in a small number of streetsegments (Sherman et al. 1989, Weisburd and Green 1994, Spelman 1995, Weisburd andGreen 1995, Block and Davis 1996, Eck et al. 2000, St. Jean 2007, Braga et al. 2010,2011).

This study is carried out in this vein to further the micro-scale approach in the geog-raphy of crime in general, and micro-scale hotspot detection in particular, and aims todevelop a new type of hotspot detection method that allows us to investigate the micro-spatial concentration of crime incidents within each street segment and also explore theirtemporal patterns over a period of time. The study shares the same underlying assump-tion with other micro-scale approaches that the outcome of crime hotspot detection in amicro-space setting provides a new insight into the characteristics of crime distributionswith greater precision, which cannot be obtained through the application of a conventionalmethod that relies on aggregated areal data (Weisburd et al. 2004).

In addition to the notion of spatial concentration of incidents, literature on the geogra-phy of crime recognises that crime incidents tend to exhibit temporal concentrations also(Brantingham and Brantingham 1991, Eck and Weisburd 1995, Ratcliffe and McCullagh1998). Recent studies on micro-scale variations indeed suggest that crime hotspots acrossmicro-places tend to remain in the same or similar locations over time (Spelman 1995,Robinson et al. 2003, Johnson and Bowers 2004, Weisburd et al. 2004, 2009b, Groff et al.2010). They confirm the importance of the simultaneous investigation of the spatial and thetemporal aspects of crime, or the introduction of time-adjusted methods for gaining a morecomprehensive understanding of crime hotspots in a micro-setting (Johnson et al. 2008).Grubesic and Mark (2008) report that spatial-temporal approaches are not only capable ofsupplying additional information about the nature of the offences, but also provide cluesabout the behaviour of perpetrators. There are a few studies that focus on micro-scalespace-time analysis including Ratcliffe (2005), who presented a method for measuring themovement of crime patterns over time using individual crime data. However, compared tothe spatial dimension of crime hotspots, the space-time dimension of crime hotspots stillhas much to be investigated.

Ratcliffe (2002) reports that crime hotspots that are close to each other may in fact havedistinctly different temporal patterns from one another. Similarly, Groff et al. (2010) reportthat the concentration of a high volume of cases on a street segment may follow a temporaltrajectory that is unrelated to those in its immediate adjacent streets. While these studiesconfirm area-to-area or street-to-street variability of the temporal trajectory of crime inci-dents, the variation can be observed at an even finer scale. For instance, Shiode (2011)pinpoints a single street address among the entire street network in the study area as thehottest spot for drug-dealing activities over a 2-year period and identifies the location as ahotbed (chronic locations for call to police) of drug dealing. Based on these findings, thisstudy uses street-address-level data for space-time hotspot detection with the assumptionthat analysis with disaggregate data could reveal a highly localised variation in the distribu-tion of crime incidents at a scale that is smaller than street segments. Shiode (2011) points

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868 S. Shiode and N. Shiode

out that the locations of crime incidents are confined by the layout of the street networkand, therefore, would be more appropriate to apply the network metric that is governedby the structure of and the distance along the street network, as it is expected to improvethe level of accuracy for measuring the spatial relationship between individual crime inci-dents. There are a number of cases in crime analysis that may be better addressed using thenetwork metric rather than the two-dimensional (2D) Euclidean metric, and these includestreet robbery and street-level drug dealing, among other types of crimes.

Several methods are commonly used for detecting crime hotspots, and these includelocal autocorrelation methods (Ratcliffe and McCullagh 1999, Craglia et al. 2000), kerneldensity estimation (McLafferty et al. 2000, Ratcliffe 2005, Johnson et al. 2008), k-meansclustering, and Spatial and Temporal Analysis of Crime (STAC) (Block 1995, Block andBlock 1995). STAC is widely used (Rich 1995, Ratcliffe and McCullagh 2001, Williamsonet al. 2001), partly because of the simplicity and clarity of its concept (Block 2000) andalso because it is readily available through a comprehensive crime analysis tool calledCrimeStat (Levine 2010). STAC adopts a search-window approach to carry out hotspotdetection. A conventional, regular search window defined in the 2D space takes the formof a circular or an ellipsoidal sub-area, which discretely and exhaustively sweeps acrossthe study area in such a way that the window constantly covers a fixed amount of area.While STAC was designed specifically for its application in crime science, the techniqueof search-window-type searching itself has been adopted widely in other fields also, owingto its intuitively comprehensible concept as well as the methodological flexibility that facil-itates its adaptation to other contexts; some notable examples are Geographical AnalysisMachine (GAM), a pioneering work of its kind (Openshaw et al. 1987), and spatial scanstatistics (SaTScan) developed in spatial epidemiology (Kulldorff and Nagarwalla 1995,Kulldorff 1997, Block 2007) and its variants with more flexibility in the shape of theirsearch window (Duczmal and Assuncao 2004, Patil and Taillie 2004, Tango and Takahashi2005, Kulldorff et al. 2006, Takahashi et al. 2008). Taking into consideration their preva-lence in the relevant fields and the methodological adaptability to space-time networkanalysis, this study extends the search-window-type methods to accommodate searchesin the network space and also in the temporal dimension of a micro-scale setting with ascope to offer an alternative to the conventional search-window-type methods, includingGAM and STAC, for crime hotspot detection.

As an example of an extended search-window-type method, Shiode (2011) developed anetwork-based, street-level search-window-type method and demonstrated that it can detecthotspots more accurately and in a more stable manner than the conventional Euclidean-based methods could when applied to disaggregate, address-level data in a micro-scalesetting. The paper also suggested that adding the temporal information could provide aclearer picture of the patterns of crime occurrence and made some observation over thestability of some hotspots over two consecutive time points. However, it failed to simul-taneously account for the concentration of crime incidents over space and time. In spiteof the presence of a wide range of search-window-type methods, none of them have beenextended to both the network space and the space-time dimension so far.

Network-based analysis is a type of analysis where the network metric plays a key rolein measuring the distance using the shortest-path distance between events that are assumedto be embedded in the network space. Network-based methods have seen a rapid method-ological advancement with an increasing range of applications over the last two decades,and several studies have confirmed the significance of introducing the network dimensionin the analyses of events observed on a network. Applications of network-based analy-sis now cover a wide range of research topics such as traffic accident analysis (Okabe

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and Satoh 2006, Steenberghen et al. 2009, Dai et al. 2010), urban facilities (Okunuki andOkabe 2003, Shiode 2008, Shiode and Shiode 2009), wildlife fatality (Clevenger et al.2003, Ramp et al. 2005, Langen et al. 2007), landscape ecology (Spooner et al. 2004,Maheu-Giroux and de Blois 2007), topography (Shiode and Shiode 2011), health (Shiode2012) and a host of other applications listed by Okabe and Sugihara (2012); however, itsapplication in crime analysis is still limited. One of the few attempts has been made byOkabe et al. (2009), who developed and applied the network-based Kernel density methodto the distribution of crime incidents. Although the events analysed in the above studiesseem to follow a distinct temporal pattern, none of these studies have attempted to incor-porate the temporal dimension to the analysis of the point pattern in addition to the networkdimension they have accounted for in their studies.

It is against this background that this study proposes a new analytical method forspatial-temporal analysis of crime hotspots. It builds on a recently developed hotspot detec-tion method that was designed to analyse non-temporal, street-level spatial distribution ofcrime incidents (Shiode 2011) and extends it to the temporal dimension to analyse a disag-gregate space-time distribution of crime incidents observed on a street network over spaceand time.

The rest of the study is organised as follows. The study first introduces the concept of anetwork-based space-time search window by extending the conventional search-window-type technique to enable micro-scale analysis along the street network across space andtime. A simulation study is conducted to investigate the validity of the proposed methodand its relative advantage over its non-temporal counterpart. This is followed by a casestudy using street-address-level data of drug dealing and assaults in Buffalo, New York,to explore whether the proposed method can help provide an insight into the micro-spatialand micro-temporal patterns of crime. The study concludes with a summary of findingsand a discussion on future research directions.

2. Detecting crime hotspots with network-based search windows

This section outlines the conceptual framework as well as the methodological details of theproposed method. It is aimed at modifying a conventional search-window-type method tocarry out analyses in the space-time dimension whose spatial dimension is confined by thestreet network.

2.1. Network-based spatial search window (SNT-SW) and network-based space-timesearch window (STNT-SW)

A search window introduced in this study generally refers to a sub-area of a fixed sizethat can be used for sweeping across the study area and detecting high concentration ofcrime incidents in a small space. Unlike a conventional search window that usually takesa circular or ellipsoidal shape, Shiode (2011) proposed a network-based search windowthat takes the form of a sub-network, or a collection of line segments, whose total lengthremains the same but its form changes and flexibly follows the structure of the network asit sweeps along. While a circular search window is used for sweeping across a study areadefined by the 2D Euclidean plane, a network search window moves along a network andcaptures incidents that are found within the extent of the network search window in a singleinstance.

The search windows can be also generalised with respect to the temporal durationthey account for. When the notion of a conventional search window is extended to searchthrough the space-time dimension, it will take the form of a cylindrical search window

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Euclideanspace-timesearch window

Euclidean spacesearch window

Network-basedspace-timesearch window

Network-basedspace searchwindow

Figure 1. Illustration of a conventional search window (lower left), a network-based search window(lower right), a conventional space-time search window (upper left) and a network-based space-timesearch window (upper right). The spatial search windows are formed on and sweep across the 2Dplane of the study area, while their space-time equivalents search through the space-time cube.

whose circular segment in the horizontal direction covers the spatial extent while its heightor the amount of vertical extrusion covers the temporal extent (Kulldorff 2001). By apply-ing the same principle, the notion of a network search window can be also extended andextruded in the vertical direction along the temporal axis so that it can search throughthe space-time dimension. Figure 1 shows an illustrative example of a conventional searchwindow, a network-based search window, a conventional space-time search window and anetwork-based space-time search window. The network-based search window covers partof the street network in such a way that its total length remains the same, while its space-time equivalent is formed by extruding it in the vertical direction. Since they are formedalong the street network, both search windows are confined by the layout of the networkand change their shape accordingly as they move along the network. In order to avoid con-fusion, this study hereafter refers to the network-based spatial search window as SNT-SWand the newly developed network-based space-time search window as STNT-SW.

Suppose that N s denotes the entire network in the study area and ws is an SNT-SW thatsweeps across N s. ws should satisfy the following conditions:

(1) ws is a single continuous sub-network; i.e. any pair of points in ws are connectedby at least one path.

(2) ws has a fixed length c (hereafter called the window size), which is less than orequal to the total length of the study area; i.e. |ws| = c for 0 ≤ c ≤ |Ns|, where |ws|denotes the length of ws, that is, the total length of all line segments comprising ws

at any instance.

The definition of STNT-SW can be extended from that of SNT-SW. Suppose that N st denotesthe entire space-time network of the study area, where N s and T represent its spatial extent

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and its temporal duration, respectively. Let wst be an STNT-SW that sweeps across N st. wst

should satisfy the following conditions:

(1) wst is a single continuous space-time sub-network; i.e. any pair of points in wst areconnected by at least one path.

(2) wst has a fixed window size, consisting of two constants c in space and t in time,where c and t are less than or equal to the total length of the given network andthe time period, respectively; i.e. |wst| = f (c,t) for 0 ≤ c ≤ |Ns| and 0 ≤ t ≤ |T |,where |wst| denotes the size of wst.

Shiode (2011) defines crime hotspots as ‘a finite area along the street network with asignificant level of elevated crime incident counts that are detected through a statisticalprocedure’ (Shiode 2011, p. 368). This study uses the same definition and assumes, as thenull model for detecting hotspots, homogeneity of the distribution of crime incidents onN st (i.e. no significant concentration of crime incidents exists along the network). Underthis assumption, a set of points that follow the homogeneous binomial process are gener-ated on N st with parameters n and p, where n is the number of points placed on N st (i.e. thenumber of crime incidents that took place on N st) and p = |wst|/|N st| (where |wst| ≤ |N st|)is the ratio of the size of STNT-SW to the overall size of N st. Let Xwst be the numberof points that fall in wst. Then, the probability of finding x number of crime incidentswithin wst is

P[Xwst = x] = nCx(p)x(1 − p)n−x = nCx(|wst|/|Nst|)x(1 − |wst|/|Nst|)n−x,

where x = 0, 1, . . . , n.(1)

It is known that the probabilities from the binomial distribution can be rounded to thosefrom the Poisson distribution when n is sufficiently large and p is small. By using a largenumber of crime incidents and adopting a relatively small wst in relation to N st, the dif-ference between the two probability distributions calculated from the data should becomenegligible. Therefore, this study assumes the homogeneous Poisson process, i.e.

P[Xwst = x] = e−λ λx

x! , x = 0, 1, . . . , n, λ = np = n |wst| / |Nst| (2)

where λ is the expected number of crime incidents within wst.STNT-SW is generated around a set of pre-defined locations hereafter called reference

points. While reference points for SNT-SW consist of a set of points identified at a constantinterval along N s, reference points for STNT-SW are placed at a constant interval alongN s and these are repeated at a constant interval in the vertical direction on N st to coverthe entire temporal duration of T . The process of constructing STNT-SW firstly followsthat for SNT-SW in the spatial dimension. This is based on the shortest-path tree search(Dijkstra 1959, Aho et al. 1983), where the search sweep extends from each reference pointin every possible direction along the network paths until the size of the shortest-path tree(or the cumulative length of all links covered by the search window) reaches |N s| (Shiode2011). Once SNT-SW is constructed, it is extended in the temporal direction to match thepre-defined temporal duration of t.

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2.2. Hotspot detection with two network-based search-window-type methods:SNT-STAC and STNT-STAC

Using the concept of STNT-SW, this study introduces a new type of hotspot detectionmethod by developing the space-time network equivalent of a conventional search-window-type method. Although the method developed in this study has its methodological root ingeneral search-window techniques, this study will compare the new technique specificallyto one of these methods widely used in crime science, STAC (Block 1998, Levine 2010).The two network-based methods addressed in this study are hereafter called the network-based spatial STAC (SNT-STAC) and the newly developed network-based space-time STAC(STNT-STAC).

The conventional Euclidean-based STAC uses a circular search window of a fixed sizeto detect hotspots by identifying places with a significant concentration of crime incidentsthat exceeds a pre-defined threshold, and it then calculates the best-fitting standard devia-tional ellipses (hotspot areas) to represent the detected overlapping search windows. Theconventional STAC takes the following steps to detect hotspots (Block 1998, Craglia et al.2000, Levine 2010):

(1) Add 400 reference points within the boundary of the study area at a regular intervalby laying out a 20-by-20 grid of points.

(2) Place a circular search window of a predetermined radius around every referencepoint.

(3) Count the number of data points captured by the search window at each referencepoint location.

(4) Record at most 25 circles that captured more number of data points than thethreshold value.

(5) Sort the recorded search windows in descending order by their point counts. If apoint belongs to more than one search window, all points within the adjacent searchwindows will be combined to form a cluster of points known as a hot cluster.

(6) Calculate the best-fitting standard deviational ellipses for representing the crimeincidents within each hot cluster.

The procedure for detecting space-time hotspots using STNT-STAC can be designed ina similar manner. The steps designed specifically for STNT-STAC are those on (1) thepositioning of the reference points along N st, (2) use of a network-based space-time searchwindow wst, (3) detection of the hotspots through a statistical test using theoretical pointdistribution rather than those obtained through Monte Carlo simulations adopted in STAC,and (4) representation of hotspots in the form of overlapping detected hotspots (i.e. thenetwork-based space-time equivalent of a hot cluster), rather than the best-fitting standarddeviational ellipses. This study sets the threshold value for STNT-STAC at the level that isstatistically significant under the null model of the space-time Poisson process. Under thenull hypothesis that Xwst is an independent Poisson random variable with the expected valueof λ, the cumulative probability of having at least x number of crime incidents observed inwst is

P[Xwst ≥ x] = 1 − P[Xwst < x] = 1 −∑x−1

k=0e−λ λk

k! (3)

If the cumulative probability calculated for the observed incidents within wst is less than thesignificance level α, then the null hypothesis is rejected and these incidents are consideredto form a hotspot.

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3. Hotspot detection with a simulated crime incident distribution

A proprietary computer program was coded for executing STNT-STAC. This program wasused in the simulation study as well as the empirical case study described in a later sec-tion. In order to examine the relative advantage of STNT-STAC in detecting the simulatedhotspots with higher accuracy, SNT-STAC proposed by Shiode (2011) was also carried out.While no direct comparison with the conventional Euclidean-based STAC was performedin this study, the relative advantage of SNT-STAC over Euclidean-based STAC has beenassessed in our previous study (Shiode 2011).

3.1. Simulated clustered point patterns: the space-time Poisson cluster process

In order to examine if the proposed method can accurately detect space-time clusters,STNT-STAC was applied to a set of simulated point data whose distribution pattern and thespace-time cluster locations within are known. Among the various types of point processesknown in the literature on the spatial point process (Cliff and Ord 1981, Boots and Getis1988, Cressie 1991), this study adopts the Poisson cluster process (Upton and Fingleton1985, Diggle 2003). The composition of the Poisson cluster process used in this study fol-lows that of a regular Poisson cluster process in that it adopts what was originally designedfor a point distribution on a flat plane but applies it instead to the network space defined inthe space-time dimension. Adaptation of the Poisson cluster process defined on a flat planeto the network space was carried out by Shiode (2011), and this study further extends itto that in the space-time dimension, in which a set of points are placed on N st. A sim-ulated distribution of street-crime incidents can be thus produced through the followingthree steps:

(1) Generate the reference locations, or parent points (Diggle 2003), around which theclusters are generated. Identification of the parent points is realised by randomlyplacing a fixed number of points on N st.

(2) Generate a set of points called offspring points (Diggle 2003) around each parentpoint. In the space-time setting, a fixed number of offspring points are randomlyplaced on a set of space-time sub-networks, each of which occupies a fixed lengthof sub-network and temporal duration on N st.

(3) Generate a uniform random distribution of points on N st and superimpose themon the offspring points. This produces a simulated distribution of the locations ofhypothetical crime incidents.

The spatial extent N s of N st covers the same street network as that used in the simula-tion analysis by Shiode (2011), which is part of a street network in downtown Buffalo,New York. It consists of a street network that covers a total of 41,530 ft of street seg-ments within a rectangular study area of 3000 ft by 2500 ft. This study adds the temporaldimension to the study area and sets the time frame of N st at one year. Figure 2 showsthe simulated space-time Poisson cluster points, where 12 locations are randomly selectedas the parent points (Figure 2a) which identify the respective line segment to host theoffspring points in the spatial direction, and each parent point is assigned a differentmonth of the year to give temporal variation. A total of 200 offspring points are randomlyassigned between the 12 space-time sub-networks (Figure 2b). Finally, 100 points are ran-domly placed on N st, which, together with the offspring points, form an inhomogeneousspace-time Poisson clustered point pattern consisting of 300 points in the space-time cube(Figure 2c and d).

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Figure 2. A simulated distribution of 300 space-time Poisson clustered points generated along thestreet network of downtown Buffalo, New York, to represent hypothetical street-crime incidents: (a)12 parent points (white circles) and the respective street line segment each point is contained within(grey lines), which serve as the space-time sub-networks to be populated with hypothetical crimehotspots, (b) a 3D projection of 200 offspring points randomly assigned across the 12 space-timesub-networks and presented in the space-time cube, (c) a 2D projection of 300 space-time Poissonclustered points obtained by superimposing 100 randomly generated points (grey dots) on the 200 off-spring points (black dots), and (d) a 3D projection of the 300 space-time Poisson clustered pointspresented in the space-time cube.

3.2. Application of STNT-STAC and SNT-STAC to the simulated point distribution

Using the simulated clustered point distribution, the performance of STNT-STAC is com-pared with that of SNT-STAC. In order to apply the two methods under the same condition,reference points for SNT-STAC are generated by placing points at every 100 ft over N s

which produces approximately 400 reference points, whereas the reference points forSTNT-STAC are generated at the same locations as those for SNT-STAC for the spatialdimension and approximately 360 points along the temporal dimension. The size of ws

should be larger than the interval between the reference points so that there will be a suffi-cient amount of overlap between the nearby search windows, yet small enough to be ableto detect spatial variations within a single street segment. The spatial extent of wst shouldbe consistent with that of ws and its temporal duration should be decided at a length thatallows detection of a sufficient number of incidents to form a hotspot, yet short enough to

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Figure 3. The spatial and the spatial-temporal hotspots detected respectively with SNT-STAC andSTNT-STAC among the simulated distribution of 300 space-time Poisson clustered points generatedalong the street network of downtown Buffalo, New York: (a) a 2D projection of the network-basedspatial hotspots (green lines) and the network-based space-time hotspots (red lines) and (b) a 3Dprojection of space-time distribution of the 300 hypothetical crime incidents in dots using gradatedcolours (the warmer the colour, the later in the year the incident took place) and the network-basedspace-time hotspots (blue rectangles).

be able to detect short-term outbursts of crime incidents. The size of the search windowwas determined through an exploratory process, and after several attempts at finding theright balance, it was fixed at 300 ft for ws and at 300 ft and 14 days for wst.

Figure 3a compares the hotspots detected by SNT-STAC (green lines) and those detectedby STNT-STAC (red lines). They are the results of hypothesis testing at 5% significancelevel for both methods after correcting the significance level to achieve an overall 5%of the significance level through Bonferroni adjustments for the effect of multiple test-ing. Figure 3b shows a 3D projection of the simulated point distribution and the hotspotsdetected by STNT-STAC (blue rectangles). Visual examination of the figures reveals thefollowing:

(1) STNT-STAC detected 11 clusters and SNT-STAC detected 10 clusters out of the12 hotspots produced in the simulated distribution. Neither method succeededin detecting the simulated cluster for August. This is primarily because, duringthe process of scattering random points uniformly among all offspring points,the space-time sub-network for August received less number of points by chancecompared to the other locations.

(2) STNT-STAC detected the simulated space-time hotspot for December, whereasSNT-STAC failed to detect it as a spatial hotspot. This confirms that STNT-STACcan detect hotspots more accurately in a micro-spatial and micro-temporal setting.

The space-time hotspots detected by STNT-STAC provide additional description to thedetected spatial hotspots as to when they form hotspots within the given temporal dura-tion. The results also demonstrate that STNT-STAC can detect space-time hotspots that arenot spatially clustered, which suggests that some concentrations of crime incidents that arefocused to specific space-time spots may remain undetected if only SNT-STAC were to beapplied.

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4. Case study on drug dealing and assault incidents

Following the outcome of the simulation study that confirmed the significance ofSTNT-STAC, this section applies both methods to the empirical analysis of street-crimedata to gain an insight into their distributions and further verification of the significance ofSTNT-STAC.

4.1. Data description

The study area used in this case study is a relatively compact urban area of 5000 ft by5000 ft square, taken from the downtown area of City of Buffalo, New York. The streetnetwork in the study area runs for a total length of 52,574 ft. The data used in this study arecall-for-service records (911 emergency call records) from downtown Buffalo includingthe study area in 1996. Among the various types of offences in the 911 records, this studyaddresses two types of common crimes: drug dealing and assaults. Both are high-volumeoffences but are expected to show a stark contrast in their distribution patterns, which mayhelp illustrate how the proposed methods detect hotspots differently, if at all, for differ-ent distribution patterns. Within the study area, 410 cases of drug-dealing incidents and550 cases of assault incidents were recorded in 1996.

4.2. Applying STNT-STAC and SNT-STAC

As in the case of the simulated point data, some of the parameters require adjustments priorto the application of the network-based methods. In the case of STNT-STAC, the referencepoints are placed at a 150 ft interval along the street network of the study area to gener-ate a total of approximately 850 points, and searches are made around all reference pointsusing SNT-SW of 300 ft, which is decided at a level that is sufficiently small for detectinghotspots formed at a scale smaller than each street segment. STNT-STAC searches aroundthe reference points of approximately 850 points in the spatial dimension and approxi-mately 350 points in the temporal dimension, with STNT-SW of 300 ft and 14 days, whichis also decided at a level that is sufficiently small for the purpose of the analysis.

Figure 4a and b shows the results from the application of SNT-STAC and STNT-STACon the drug-dealing cases. SNT-STAC revealed that 9.6% of the entire street networkwere detected as significant hotspots, confirming that crime is highly concentrated onmicro-places, as suggested in the literature. STNT-STAC revealed that only 0.25% of thespace-time network were detected as significant space-time hotspots, which indicates thatthe space-time hotspots are concentrated in an even smaller number of specific space-timeplaces. Secondly, the distribution pattern of the space-time hotspots detected through STNT-STAC gave a deeper insight into the description of these hotspots than the non-temporalspatial hotspots did. For instance, the recurrent appearance of space-time hotspots aroundthe centre of the study area revealed the stable and persistent nature of the drug markets.While both STNT-STAC and SNT-STAC have successfully detected the hotspots at theselocations, SNT-STAC did not provide information on their temporal patterns (Figure 4a).Finally, the comparison between the outcomes of the analysis using the two methodsrevealed that many of the spatial hotspot locations were undetected under the space-timesearch (Figure 4b). This suggests that the majority of non-temporal spatial hotspots areformed by crime incidents with low temporal concentration but are sufficiently high involume when aggregated over the entire study period.

The two methods were also used for analysing the distribution of assault incidents. Theresults show quite different patterns of hotspot locations from those of the drug markets

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(a) (b)

Figure 4. The spatial and the spatial-temporal hotspots detected respectively with SNT-STACand STNT-STAC among the 410 cases of drug-dealing incidents recorded in downtown Buffalo,New York, in 1996: (a) a 2D projection of the network-based spatial hotspots (green lines) and thenetwork-based space-time hotspots (red lines) of drug-dealing incidents and (b) a 3D projection ofthe space-time distribution of the drug-dealing incidents in dots using gradated colours (the warmerthe colour, the later in the year the incident took place) and the network-based space-time hotspots(brown rectangles).

(a) (b)

Figure 5. The spatial and the spatial-temporal hotspots detected respectively with SNT-STAC andSTNT-STAC among the 550 cases of assault incidents recorded in downtown Buffalo, New York,in 1996: (a) a 2D projection of the network-based spatial hotspots (green lines) and the network-based space-time hotspots (red lines) of assault incidents and (b) a 3D projection of the space-timedistribution of the assault incidents in dots using gradated colours (the warmer the colour, the laterin the year the incident took place) and the network-based space-time hotspots (blue rectangles).

(Figure 5a and b). In the case of assaults, 6.0% of the street network were detected assignificant non-temporal spatial hotspots, whereas 0.09% of the space-time network weredetected as significant space-time hotspots. This means that STNT-STAC identified even asmaller portion of the space-time network as significant space-time hotspots compared tothe case of drug dealing for which 0.25% of the entire network were detected as space-timehotspots. It also showed that, unlike the drug markets, no recurrent space-time hotspots of

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assaults were observed at a single location. In fact, STNT-STAC detected only three space-time hotspots (Figure 5b) whose temporal duration was 17, 12 and 21 days, respectively(days 111–127, 169–190 and 240–260), which suggests that assaults are more scatteredacross the ST-NT cube than drug dealing is. In addition, as in the case of the simulationanalysis, STNT-STAC detected a space-time hotspot that was not picked up by SNT-STACas a spatial hotspot. This is due to a sudden surge in the number of offences over a shortperiod of time (July–August). While this particular space-time hotspot does not show anexcessively high concentration of offences, it demonstrates the capacity of STNT-STAC todetect spatially non-significant but spatially and temporally significant hotspots.

5. Conclusions

This study developed STNT-STAC, a network-based, space-time hotspot detection methodthat extended the notion of search-window-type methods. The study first described theconceptual as well as the methodological framework of the new methods, and it then carriedout analyses using two sets of data: (1) a simulated space-time clustered point distributionand (2) street-crime incident data from Buffalo, New York.

The results from the simulation study suggest that the proposed method can detect thespace-time crime hotspots at the street-address level more accurately than its non-temporalcounterpart could, pinpointing where and when crime incidents are concentrated. It alsogives an insight into the pattern of concentration and dispersion of the incidents withineach spatial hotspot during the study period. The detected space-time hotspots provideadditional information on time and location that require focused attention at the street level.For instance, they may be linked to crime-inducing factors that are space-time specific.Identifying the pattern of space-time hotspot occurrences may help reveal such factors,thus contributing to the future planning of crime-reducing strategies.

The case study using the empirical data illustrated the contrast between the distributionpattern of two types of street crime: drug dealing and assaults. The recurrent appearance ofspace-time hotspots of drug dealing in specific locations confirms the stability of drug mar-kets. The empirical analysis also revealed the scattered nature of assault incidents, whichformed a much smaller number of space-time hotspots with no recurrent concentration.This result suggests that a highly focused investigation on specific space-time hotspotsmay prove less effective for this type of crime.

Finally, both the simulation study and the case study demonstrated that space-timehotspots may be detected with STNT-STAC at locations where no significant spatialhotspots were found with SNT-STAC. These space-time hotspots are formed primarilyby a sudden increase in the number of offences that lasted for only a short period oftime. Although they were not detected as significant non-temporal spatial hotspots, a closeexamination of circumstances surrounding these occurrences may help prevent or reducethe repetition of such spatially and temporally concentrated outbursts of crime in future.Interestingly, the case study also showed an opposite scenario; that is, some spatial hotspotlocations were found by SNT-STAC in places where no significant space-time hotspots weredetected by STNT-STAC. This indicates that a sufficient number of incidents were recordedin a small area, but no significant concentration within a short period of time was observedamong these incidents, thus confirming the presence of warm spots, or areas with persis-tent occurrence of crime incidents that also require attention. Both scenarios demonstratethat using the two network-based methods together and comparing the difference in theiroutcomes can help reveal more detailed micro-scale characteristics on crime patterns thatwould have otherwise remained undiscovered.

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There are several limitations and possible future directions stemming from this study.First, the method developed in this study does not account for the relative risk, or theproportion of the crime incidents to population at risk in the respective area. The rawcrime counts and relative risk play an equally important role in policing scenes, as theformer is useful for the effective deployment of police resources to meet operational needs(Craglia et al. 2000), while the latter is useful for devising an effective policing strategy forcrime reduction in areas with elevated risk of victimisation. Methodologically, it is possibleto incorporate the relative risk within a more general framework of search-window-typemethods; however, the nature of the relative risk varies by the type of crime and estimationof the relative risk assumes knowledge of the underlying geography including the locallandscape and environment as well as activities that take place within the area. As theprimary purpose of this study is to propose a new method, estimation of the relative riskin a specific crime context is beyond its scope, even though it would form an interestingfuture challenge.

Second, as with many other search-window-type methods, multiple testing is an issuefor the method proposed in this study. Bonferroni adjustments are known to be conserva-tive for highly correlated test statistics such as those derived in this study. If a less biasedsignificance level were to be applied, it is expected that more hotspots are detected as statis-tically significant. A test with less conservative correction would detect hotspots obtainedwith Bonferroni adjustments as well as additional hotspots, which together may providemore useful information for practical policing. The method would therefore benefit frominvestigating the application of less biased approaches. These include the application of(1) an alternative method that is more suitable for an adjustment for multiple and depen-dent tests such as the false discovery rate controlling procedure and its variants, and thoserecently developed for controlling large-scale multiple testing; or (2) a statistical methodsimilar to those adopted in scan-statistic-type methods.

Third, the computer program developed in this study enables further testing of therobustness of the method. For instance, the proposed methodology was assessed with only asingle pattern of simulated clusters. It is worth investigating whether the difference betweenSTNT-STAC and SNT-STAC shown in this paper would be sustained for different sets ofsimulated data with different space-time characteristics. Use of other empirical data wouldalso help discover the space-time characteristics of crime incidents which were previouslyunknown. This includes (1) a follow-up on the differences between assaults and drug-dealing offences found in this study, (2) investigations of different space-time concentrationpatterns of different crime types, and (3) investigations of the temporal characteristics ofcrime occurrences such as the effects of seasonality and periodicity.

Finally, the set of parameters used in the empirical analysis would benefit from furthercalibration. The size of the space-time search window, for instance, can be generalised andmade variable. Although Shiode (2011) indicates that a small change in the size of thespatial search window does not significantly alter the location or the size of the hotspotsdetected, variation in the size of the search window within its possible range and its impacton the outcome should be explored more systematically. The same applies to the temporaldimension of the search window, whose sensitivity to the size of the space-time searchwindow should be also examined further.

AcknowledgementsThe authors greatly appreciate the valuable advice and comments from the anonymous referees. Thisresearch was supported in part by the Canon Foundation in Europe.

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