CRIME HOT SPOT ANALYSIS AND
DYNAMIC PIN MAP
Anak Agung Gde Agung
Rutgers University
Abstract
This paper presents three alternative methods to analyze the spatial and
temporal patterns of crime with the goal of dentifying areas with high number of
incidents. The first method is to count the number of nearby incidents from each
event, the second method is to calculate the mean and standard deviation of time
lags between two events, and the third method is to calculate the total distance
of nearest events from each incident. With Avenue programming in Arcview and
Spatial Analyst, the analysis of "hot spots" is completed for a sample
of data from police offense reports. The main conclusion of this paper is that
crime hot spots should be defined not only by the geometry of previous events
but also by their temporal characteristics.
Introduction
A crime hot spot is generally defined as an area containing dense clusters of
criminal incidents. Identifications of hotspots helps public safety institutions
allocate resources for crime prevention activities. This geographical analysis
is usually made based on crime pin maps of reported crime events over a certain
period.
The main issue in the traditional method of hot spot analysis is
the lack of time dimension to be explicitly considered (Illinois Criminal
Justice Information Authority, 1993). A hot spot is determined only by the
geometry of previous events. This simple approach may be good enough to analyze
data over a short time period, but to analyze data over a year or longer period,
crime hot spots should be determined not only by the geometrical aspect of the
events but also by their time characteristics.
One common method used to
define crime hot spots is to draw circles from each event and then find the
ellipse representing the highest density of crime, i.e., to measure events per
square mile. This method usually uses a cut-off figure, for example, only the
top 25 percent of circles containing the highest number of incidents are defined
as a hot spot. The result is an ellipse with no direct comparison with the
surrounding area.
Defining a crime hot spot is an intuitive process,
however, a definition only based on the number of events is insufficient. This
paper discusses three alternative methods to define crime hot spots. The first
method considers the number of events, the second method involves a temporal
dimension measured by the mean and standard deviation of time lags between two
events. The third method considers the relative distance between events.
Assuming the three aspects of analysis to be complementary in defining crime hot
spots, this paper compares the hot spot maps derived by these three methods.
Method 1: Crime Event Counts
In the first method, a crime hot spot is defined as the area where the number
of nearby incidents is high. The first question in dealing with this definition
is how to choose "near" events from each incident. One extreme is when
"near" is only for the location of each event itself, therefore every
event will be a hot spot. The other extreme is when we take all events, with the
result that no hot spot area can be defined.
The basic idea of counting the number of events or measuring event density in
this method is similar to the approach used in the STAC! program (Illinois
Criminal Justice Information Authority, 1993), but it is different in the
approach to deliniate the hot spots. In the STAC! program, the user define a
grid size and then divide the area into this grid. A circle is made on every
node and then the program counts the number of incidents in each circle. The
circles in the top 25% in terms of incident numbers are then defined as hot
circles. These steps are repreated for larger size of grid to get the second set
of hot circles. Combination of the two hot circles will give an ellipse or the
hot spot with greatest number of incidents.
The method used in this
paper counts the number of events within a certain distance from each event and
then store this count in that event. The test uses 2000 feet to represent the
size of three- to five-blocks of an urban area. After the number of surrounding
events are counted from each event, the next step is to use spatial
interpolation between events in order to make a continuous surface showing the
relative level of hot spots in the area. In Avenue, the main part of this method
can be written as follows:
for each frompt in
theVTab
fromShape=theVTab.ReturnValue(theShapeField,frompt)
totalEvents=0
for each topt in theVTab
toShape=theVTab.ReturnValue(theShapeField,topt)
theDistance=(FromShape.Distance(toShape))
if (theDistance < 2000)
then
totalEvents=1+totalEvents
end
end
end
Method 2: Time Lag Between Events
In the second method, I define a hot spot as an area where the frequency of
crime incidents is high and/or occur on a relatively regular basis. This can be
measured by the mean and standard deviation of the time lag between two
consecutive incidents, in which a low mean represents a high frequency of crime
and low standard deviation means more regular incidents. As in Method 1, this
approach requires us to determine the search distance from each incident.
In Avenue, the main part of this method can be written as follows:
searchwithin = 2000
for each frompt in
theVTab
' Before time is calculated, we need to sort the events by date
' This will be from DateList, a list of events date
DateList = {}
meanLag=0
' searching the surounding events
for each topt in theVTab
toShape=theVTab.ReturnValue(theShapeField,topt)
theDistance=(FromShape.Distance(toShape))
if (theDistance <=
searchwithin) then
DateList.Add(RawDate)
end
end
EventCount=DateList.Count
if (EventCount > 1) then
DateList.sort(true)
theLoop=EventCount-2
totalLag=0
for each
event in 0..theLoop
Event2=Date.Make(DateList.Get(event+1),"yy/MM/dd-hhhh:m")
Event1=Date.Make(DateList.Get(event),"yy/MM/dd-hhhh:m")
theLag=Event2-Event1
theLaginHour=(theLag.AsSeconds)/3600
totalLag=totalLag+theLaginHour
end
meanLag=totalLag/(eventCount-1)
SumofSquare=0
for each event in 0..theLoop
Event2=Date.Make(DateList.Get(event+1),"yy/MM/dd-hhhh:m")
Event1=Date.Make(DateList.Get(event),"yy/MM/dd-hhhh:m")
theLag=Event2-Event1
theLaginHour=(theLag.AsSeconds)/3600
SumofSquare=SumofSquare+((theLaginHour-meanLag)^2)
end
StdDeviation=(SumofSquare/(eventCount-1)).sqrt
end
end
Method 3: Spatial Concentration of Events
In the third method, I define a crime hot spot as an area where crime
incidences are geographically concentrated. To measure the level of
concentration, I suggest to use total distance from each event to a number of
nearest incidents. To determine how many nearest incidents to be considered, we
can take a small percentage (5 or 10 percent) of total events. The following
Avenue script shows the main part of this method:
numberofNearestEvents=7
'This number is about 5 percent of
total events
for each frompt in theVTab
FromShape=theVTab.ReturnValue(theShapeField,frompt)
totalDistance=0
DistanceList = {}
for each topt in theVTab
toShape=theVTab.ReturnValue(theShapeField,topt)
theDistance=(FromShape.Distance(toShape))
DistanceList.Add(theDistance)
end
DistanceList.sort(true)
for each theNearest in
0..numberofNearestEvents
totalDistance=totalDistance +
DistanceList.Get(theNearest)
end
theVTab.SetValue(totalDistanceField,frompt,totalDistance)
DistanceList.empty
end
Implementation
The three different methods above are tested with a sample data of 200 events
obtained from theCharlotte-Mecklenburg Police Department. The data cover
offenses of homicide, rape, robbery, and aggravated assault occurring in
downtown Charlotte during the month of July, 1996. The main purpose of doing the
test is to find out whether the three methods give different results indicating
that crime hot spots should be defined by both spatial and temporal
characteristics of previous events. These sample data are taken from a
relatively short time period, but if the test shows three different results then
we can anticipate similar results if the analysis is made for annual data.
Conclusion
Figure 1, 2a, 2b, and 3 show that the three approaches are overlapping in one
area (Figure 4) that is definitely identified as a hot spot by all three
methods. The red area shown in these figures is five percent of the total area.
Method 1 and 3 show great similarity, but between these two maps and Method 2,
there are some differences. With a temporal measure, some areas in the center of
the map are identified as hot spot but not by the other two methods. These maps
also suggest that areas identified as hot spots by Method 1 and 3 are not
necessarily important in terms of Method 2.
These exercises suggest that analyzing spatial and temporal pattern of crime,
especially to define crime hot spot, is technically a simple process in Arcview.
However, there are several important issues dealing with crime data that should
be realized in this process. This analysis uses offense data, therefore a crime
hot spot is defined based only on reported incidents. The other issue is data
precision, especially for temporal information. There are many cases in which
time of incidents can only be reported within a range of time, for example
between 8am and 5pm, rather than a specific time.
..
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Acknowledgement
The author would like to thank Dr. Lyna Wiggins, Rutgers University, for her
comments and enormous support for this research and Charlotte-Mecklenburg Police
Department, Charlotte, North Carolina which provide data sample of offense
report used in this exercise.
Reference
Illinois Criminal Justice Information Authority, 1993. Spatial and Temporal
Analysis of Crime: User Manual.
Anak Agung Gde Agung
Rutgers University
33 Livingston
Avenue, Suite 544
New Brunswick, New Jersey 08901, USA
E-mail: [EMAIL PROTECTED]
