Urban Crime Mitigation

A Model to Derive Criminal Patterns and Determine Defender Placement to

Reduce Opportunistic Crime

Solomon Y. Sonya, Luke Brantley and Meagan Whitaker

Departments of Computer Science and Operations Research, U.S.A. Air Force Academy, 2534 Fairchild Drive, U.S.A.F

Academy, Colorado, 80840, U.S.A.

Keywords: Opportunistic Crime, Statistical Analysis, Frequency Distribution, Pattern Recognition.

Abstract: Urban opportunistic crime is a problem throughout the world causing financial, physical, and emotional

damages to innocent citizens and organizations. Opportunistic crimes require minimal reconnaissance and

preparation in order to conduct an attack (e.g., burglary, robbery, vandalism, and assault). Opportunistic

criminals are more spontaneous in nature making their actions difficult to anticipate and create an approach

to reduce these crimes. Statistical analysis of crimes may reveal distinct patterns from which a strategy can

be created to better mitigate future crimes. This paper describes analysis performed on real-world campus

crime data in which distinct correlations were discovered to determine the significant factors that motivate

opportunistic crime. This research concludes by developing a dynamic defender placement strategy that

adapts over time to reduce the utility of opportunistic crimes. The research contribution allows for the

determination of significant factors motivating opportunistic crime and releases a program that maps crime

occurrences over time, determines the minimum defender allocation for a given area, and dynamically

specifies defender placement strategy to mitigate future crime. The novelty of this approach allows for

application to other campuses, shopping complexes, and living districts to form conclusions about

opportunistic criminal activity and formulate an approach to abate such crimes.

1 INTRODUCTION

Opportunistic crime is a serious problem affecting

urban areas. As opposed to well-planned and

coordinated attacks (e.g. terrorist attacks or gang

influenced violence), opportunistic crimes are rather

spontaneous in nature and involve very little

premeditation enabling the criminal to execute an

attack based on the opportunities present at a given

time. For instance, you may have heard of stories

where a person momentarily leaves their phone,

wallet, or purse unattended, walks away to

accomplish a task only to return and discover that

their personal items have been stolen within minutes

of stepping away from the area. This would be an

example of an opportunistic crime in which a

criminal carries out an attack based on maximizing

their utility over the defender’s protection strategy.

A defender is a police officer or crime abatement

personnel whose presence and action is used to

reduce crime. The utility for an opportunistic crime

is defined as the motivation and expected outcome

of a criminal succeeding with the attack without

being apprehended in response to the defender’s

strategy (Chao et al, 2015), (Yildiz, 2002), (Osborne

and Rubinstein, 1994). Other types of opportunistic

crimes include burglary, robbery, grand theft auto,

trespassing, assault, and vandalism. In all, these

crimes are quite costly and produce damaging

effects on the population.

Attractiveness is used to measure the influences

of opportunistic crime around a specified area. A

region that exhibits more opportunistic crime than

another region is said to be more attractive to

opportunistic criminals. However, it is necessary to

bind several research questions around this concept

in order to better scope how to determine the at-

tractiveness of area. For instance, how is a

criminal’s utility impacted by the attractiveness of

an area and does this attractiveness remain static or

change over time? How can external influences

(e.g., holidays, special events, football, basketball,

soccer games, and campus parties) influence the

attractiveness of an area? Finally, if we can

218

Sonya, S., Brantley, L. and Whitaker, M.

Urban Crime Mitigation - A Model to Derive Criminal Patterns and Determine Defender Placement to Reduce Opportunistic Crime.

DOI: 10.5220/0005827302180224

In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems (ICORES 2016), pages 218-224

ISBN: 978-989-758-171-7

determine the significant factors that affect

attractiveness of opportunistic crime, is it possible to

deploy a better defender allocation strategy to

mitigate these crimes and if so, how and when

should we update this strategy? The goals of this

research are to study this concept in further detail.

Currently, University XYZ manually assigns the

defender placement and patrol strategy to cover the

campus in hopes of deterring crime. This approach

has proven to be quite time consuming and

ineffective at mitigating crime (Chao, Sinha, Tambe

2015). NOTE: the true name of the university is

masked to protect the identity of the school. In this

research, we devised an approach to analyze the

university crime data to create an appropriate model

that learns the significant factors affecting

opportunistic crime over time. This allows us the

ability to describe the underlying data and formulate

a dynamic assignment strategy to better reduce

crime.

The end result of this analysis reveals the

motivating factors that contributed to the

attractiveness for a criminal to commit an

opportunistic crime. Based on these factors, we are

able to calculate the placement of a visible defender

to deter future crime. This same approach can be

adapted to additional areas exhibiting opportunistic

crime such that motivating factors can be discovered

and a better patrol strategy devised to reduce crime.

2 BACKGROUND AND RELATED

WORK

The idea to examine opportunistic crime originated

from the Department of Homeland Security funded

CREATE (Center for Risk and Economic Analysis

of Terrorism Events) group, based at the University

of Southern California (USC). A new framework to

create a patrol allocation schedule around adaptive

opportunistic criminals was introduced in “Keeping

pace with criminals: Designing patrol allocation

against adaptive opportunistic criminal” by Chao

Zhang et al. In this research, Chao Zhang et al

applied game theoretic approaches on real-world

campus crime data to map the interaction between

patrol officers in moving vehicles and criminal

activity. This behavior was mapped as parameters in

the Dynamic Bayesian Network (DBN) in order to

learn the appropriate model and account for hidden

states which included the true number of criminals

and patrol officers present in the area and the impact

their presence may have on each other.

In addition to mobile police patrols around the

campus, University XYZ also employs visible, well-

identified campus security guards who remain

relatively stationary to an assigned grid location.

This research applies pattern recognition and

statistical analysis for the assignment of these

visible, pedestrious defenders whose presence at the

appropriate location is used to deter crime via

classical conditioning.

Classical conditioning is a model of learning that

deals with the automatic, instinctual response of a

person in response to apparent stimuli (Hall, 1998).

Classical conditioning is applied to this research to

hypothesize appropriate response of a criminal’s

actions as a result of a visible defender present

within an area.

The Cheater Model further helps to refine the

hypothesized relationship between defenders and

crimes. According to this economic theory, many

people may allow themselves to cheat or conduct

some form of unscrupulous activity when the

marginal utility to do so is greater than the marginal

costs and consequence of the activity (Nagin, 2002).

An experiment was held with varying levels of

monitoring over employees known to inflate the

truth about their self-reported performance. The

study showed that as perceived monitoring

decreased, cheating increased.

Additional research determined that criminals

react inversely to the number of defenders present at

a location. In “Crime and Human Nature: The

Definitive Study of the Causes of Crime,”

researchers Wilson and Herrnstein confirmed that

the defender/criminal relationship is determined by

classical conditioning. We use this knowledge along

with the Rational Cheater Model to assert that an

increase in defender presence should decrease crime

in an area. The locations of these defenders

however, will be crucial in having an impact to the

expected crime level. The following sections state

how analysis of crime data can indicate the location

at which to place a visible defender to mitigate

opportunistic crime.

3 RESEARCH HYPOTHESIS

Attractiveness of opportunistic crime may be

dependent on time, population, and the number of

defenders present during an incident. The

proportionality of crime discovered should reflect

the proportionality of defenders assigned to an area

Studying this interaction helps to predict the

likelihood of future crimes and efficiently assign

Urban Crime Mitigation - A Model to Derive Criminal Patterns and Determine Defender Placement to Reduce Opportunistic Crime

219

defenders to the appropriate areas of highest

attractiveness.

The following research questions help direct the

study of our hypothesis:

1. What effects (if any) do the following factors

have on the attractiveness of opportunistic crime:

 Time of Day: i.e., how does the time of day

affect the prevalence of crime?

 Day of Week: i.e., which days are more

likely to experience a proportionally higher

number of crime?

 Week of Year: i.e., is it possible to determine

which weeks of the year experience a higher

percentage of crime?

 Special Events: i.e., is it possible to

determine how special events (e.g.

football/basketball games, holidays, and

campus parties) influence crime?

 Physical Location: i.e., is crime uniformly

distributed across the campus area or which

areas have a greater propensity for

opportunistic crime?

2. In an area that exhibits attractiveness for

opportunistic crime, what is the minimum

number of defenders required to cover an area,

and where should we assign these defenders?

3. Given a defender assignment strategy, when

should we update the patrol allocation in order to

maintain the best utility for defenders to deter

crime?

4 METHODOLOGY

The methodology in this research is divided in two

sections: Data Analysis and Patrol Schedule

Assignment. The Data Analysis section determines

the significant factors affecting opportunistic crime

and displays crime patterns learned from the data

set. The Patrol Schedule Assignment section creates

the estimator of when and where crime may occur

and applies significant aspects of crime learned over

time to produce the dynamic assignment of

defenders to the areas exhibiting the highest

likelihood for a repeatable crime.

5 EXPERIMENT SETUP

University XYZ supplied an archive containing

three years of crime data between 2011-2013 and a

map of the university dividing the campus area into

five police patrol zones. Figure 1 depicts a very

short description of crime data received by the

university. Certain attributes regarding the analyzed

data are masked to protect the identities and

locations and individuals involved in the incidents.

Figure 1: Crime Data Subset.

The data set from the university included crimes

classified into 50 different categories of crimes. We

combined these classifications and reduced our

analysis to focus primarily on crimes relating to

Theft, Destruction of Property, and Assault

categories as these are the main types of

opportunistic crimes studied in this research. Figure

2 depicts a breakdown of this chart. Figure 3 depicts

the campus response area protected by the police

patrols. Zone A encompasses the majority of

university classrooms and laboratories. Zone B

encompasses the recreational areas including the

football and sports arenas. Zone D is the primary

location of on-campus housing. Zones C and E are

additional residential areas further away from main

campus.

Figure 2: Crime Description. Figure 3: Area Map.

6 EXPERIMENTATION AND

DATA ANALYSIS

We divide the research questions identified in

Chapter 3 into several experiments to form

appropriate conclusions regarding the underlying

data set.

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6.1 Time of Day Experimentation

This experiment determines if the hour of the day is

significant when categorizing types of crime. We

hypothesize since human activity varies throughout

the day, crime may follow a similar trend. We

performed a frequency analysis across the data set

and graphed the results in Figure 4. This revealed

how time of the day influenced the prevalence of

crime.

Figure 4: Crime Frequency Distribution by Hour.

Theft accounts for the highest occurrence of

crime within this data set mostly occurring between

1300 and 2000. The majority of destruction crimes

occur between 1900 and 0100. Finally, the majority

of assaults occur between 1900 and 0200. Overall,

we conclude the hour of the day has an effect on

crime and will remain a significant factor in our

analysis for determining the optimal defender

assignment strategy.

6.2 Time of Day Experimentation

This experiment determines how the day of the week

affects crime in various zones. We hypothesize that

if human activity varies based on the day of the

week (especially on weekends) then crime should

follow a similar trend. We isolated crimes reported

on each day of the week and further separated these

crimes into the respective zones reported for each

crime. Figure 5 depicts the frequency distribution of

crimes reported within each zone.

Figure 5: Frequency Distribution by Day of the Week.

In this experiment, we expected to see weekend

days display a greater statistical significance of

crimes than normal weekdays. However, this was

not the case from our data set. Zone A has the

highest concentration of crime. This is expected

because Zone A covers the majority of the university

area and campus buildings. With respect to each

zone however, crime remained relatively similar

across each day of the week. Since day of the week

was not observed to have a significant impact on the

number of crimes committed, this factor is excluded

from our analysis model.

6.3 Week of the Year Experimentation

Experiment 3 determines how the week of the year

may affect crime. Spring, summer, and winter

semesters are distinct times in which population

varies on a college campus. We hypothesize crime

patterns may follow the population throughout the

year. Figure 6 depicts the frequency distribution

created by separating crime occurrences by week of

the year divided into the five main patrol zones.

Figure 6: Frequency Distribution of Crimes by Week.

Crime trends within Zones A, C and D display

distinct trends pertaining to the spring, summer, and

fall semesters for the university. Considerably less

crime occurs during the summer weeks than during

the semesters for which most of the student body is

present for classes. Zone B exhibits a significant

spike in crime activity between weeks 36 through

48. Zone B contains the football coliseum. Upon

further investigation into the campus activity during

these weeks in Zone B, we discovered week 36 is

when home football games occur for the university.

In addition, many home games occur at the coliseum

during the fall semester. It is evident that crime

follows this trend as well. From this experiment, we

conclude the week of the year is a significant factor

affecting opportunistic crime.

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6.4 Special Events Experimentation

In this experiment, we wish to determine the

relationship between crimes around dates of special

events to identify the specific events that account for

a higher percentage of campus crime. We

hypothesize if crime seems to follow population,

then crime should increase during special events,

however, it is unknown if the increase in crime is

uniform for every event or which special events

account for a higher rise in crime. We first analyze

the overall times when crimes occurred to give us an

idea of the average crime distribution by hour. This

is noted as “All Crime” in Figure 7. Next, we

combine the schedule of special events for baseball,

basketball, and football games, fall move-in period,

and homecoming week to produce the frequency

distribution depicted in Figure 7.

Figure 7: Crime Distribution Around Special Events.

When comparing the average number of crimes

on a normal day, we determined baseball games,

basketball games and fall move-in period do not

have a considerable effect on crime. The average

number of crimes for homecoming week and

football games are considerably higher than the

average number of crimes per hour. We conclude

from this experiment that certain special events are a

significant factor affecting opportunistic crime.

6.5 Crime Densities via Clustering I

Experiments 5 through 7 determine the locations

within zones when and where crimes densities peak.

We created a separate address to latitude/longitude

derivation process in order to convert the recorded

addresses into coordinates for plotting and

organization into distinct clusters. The cluster

movements are tracked over time in order to observe

their patterns and distinctions.

Experiment 5 determines the specific areas with

the highest overall densities of crimes. We

hypothesize crime is not uniform, but may be

concentrated around certain areas within the

university patrol area. Discovering the locations with

highest densities of crime helps to reduce the search

space and allow concentration of defender

allocations around areas exhibiting the greatest

clusters of crime. Experiment 5 uses the Partitioning

Around Medoids (PAM) algorithm to provide a

more precise clustering of crime densities. We

represented the lines of longitude across the X-Axis

and plotted the lines of latitude across the Y-Axis.

Figure 8 depicts the result from plotting the clusters

of crime.

Figure 8: PAM Clustering Crime Densities by Location.

Clustering has proven to help identify areas of

highest attractiveness and can reduce the focus area

to locations exhibiting highest densities of crime.

6.6 Crime Densities via Clustering II

The purpose of this experiment is to identify specific

addresses with the highest overall densities of crime.

We hypothesize crime may follow streets, thus,

analyzing occurrences by street should identify

densities of crime as well. The frequencies of crime

by street are measured, a ceiling and floor function

is used to calculate the centroid address around most

crimes on each street, and then the derived

coordinates of the centroid are mapped to produce

the crime densities as shown in Figure 9.

Figure 9: Clustering Crime Densities via Street Address.

We conclude mapping crime occurrences to

streets may be used to determine the areas of highest

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attractiveness as well. We used two separate

approaches to plot the densities of crime. We used

the statistical programming environment, R, to

analyze the data and conduct the PAM clustering in

Experiment 5. We wrote a program to derive this

data and interface with Google Maps to allow the

observer the ability to view areas of highest

attractiveness along with additional parameters we

discovered during this analysis in Experiment 6. The

two separate approaches revealed the same

clustering which validated our methodology to map

criminal activity around clusters of repeated crime.

6.7 Crime Density Movement by Time

This experiment determines specific times and

addresses within each zone where crime densities

peak. We hypothesize mapping crimes to clusters

may determine areas of highest attractiveness such

that observing when crime clusters shift may

identify how to update the patrol strategy to follow

criminal behavior. Figure 10 is an overlay of

opportunistic crime observed using R and our

program to map the hour and location where crime

occurred.

Figure 10: Clustering Crime Densities Over Time.

Analysis of these clusters indicate a procedure to

map crime densities by time along street addresses

and notifies when to update the defender assignment

strategy based on the movement of crime clusters.

6.8 Data Analysis Conclusions

It is possible to determine how certain factors affect

attractiveness of opportunistic crime. The frequency

distributions and cluster analysis allowed us to make

several conclusions on how to learn details regarding

the data set. Time of day, week of year, special

events, and location are significant factors in

determining when and where crime occurs. Mapping

densities of crime as a function of time will help to

identify locations to place a defender and when to

adjust the visible defender assignment strategy.

7 DEFENDER ASSIGNMENT

This chapter incorporates the significant factors

identified in Chapter 6 to create the patrol schedule

to reduce opportunistic crimes. We require the

following information in order to make an efficient

defender assignment:

1. Proportionality of crime per street per hour

2. Acceptable crime threshold (defined by user)

3. Coverage area (CA) required for each street

4. Defender Presence Radius (DPR)

5. Defender Compression Factor (DCF)

The proportionality of crime per street for each

hour is calculated in Chapter 6. Our program

analyzes the number of incidents on every street for

each hour and normalizes this ratio across all

applicable crimes recorded to calculate this

proportionality. The user-defined threshold

represents the minimum percentage to view crimes

across the entire data series. For instance, data

analysis conducted in this research spans a few

square miles with years’ worth of recorded data. A

single crime incident within the entire data series is

statistically insignificant when making

generalizations regarding trends across the entire

population. Multiple crimes across several years

within the same area allow for a more accurate

generalization regarding likelihood of a future crime

within the same area. A larger threshold reveals a

larger prevalence of crime. Based on user specified

threshold (percentage), streets with applicable crime

events meeting the minimum threshold percentage

are populated for consideration in the defender

assignment function detailed below.

Coverage Area (CA) specifies the total length

(defined by crime occurrence clusters) required for

protection by defender(s). We used the haversign

formula to calculate the great-circle distance

between crime clusters on each street. This

identified how much space is required for protection

by a defender.

Defender Presence Radius (DPR) is the

effective distance established by a visible defender

to discourage crime (via classical conditioning). The

Defender Compression Factor (DCF) represents

the multiplicative effect additional defenders

assigned in the same coverage area have on the

DPR. For example, let the coverage area for a

particular street be 8000ft. Further, let the DPR be

800ft. A naïve defender assignment can be specified

as minimum_defender_count = CA / DPR. Thus, we

can ascertain 10 defenders are required to cover this

area. However, applying classical conditioning to

rational criminal behavior patterns, we postulate the

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223

more defenders placed on a street should increase

the individual DPR such that a criminal successively

observing only a few defenders (say 5 or 6 defenders

along the same path) could conclude additional

defenders are likely nearby. The criminal would opt

to move away from this location. This results in

successfully reducing the criminal’s utility to attack

by using a reduced number of defenders.

Opportunistic criminals subconsciously observe

the DCF and DPR to calculate their utility in

succeeding with the attack. Future research will be

required to know how the coverage area expands as

a function of the number of defenders present. In

this research, we assigned the DCF to 1.8 and DPR

to 800ft. Taking the DCF into account, we can

calculate the minimum number of defenders (d)

required with respect to coverage area for each street

(s) meeting the user’s threshold to be:

min

(d) = DCA

/ (DPR *DCF)

The aggregation of the minimum defender count

per street given a specified threshold parameter

produces the minimum number of defenders

required to protect an area and more importantly,

specifies the location at which the defenders are

assigned. Figure 11 depicts a final output from our

program displaying the assignment of each defender

for each particular hour.

Figure 11: Minimum Defender Allocation.

8 CONCLUSIONS

Opportunistic crimes require minimal

reconnaissance and preparation in order to conduct

an attack. The damages of such attacks can be

extremely costly to the population. This research

presented a new approach to apply frequency

analysis coupled with density distributions to

determine the significant factors that affect the

attractiveness of opportunistic crime and produce a

methodology to mitigate these crimes. Based on the

data set analyzed in this research, time of day, week

of year, special events, and location are significant

factors in determining when and where crime

occurs. Placement of a visible defender can be

determined by the significant factors uncovered in

this research, proportionality of crime, crime

coverage area, defender presence radius, and the

defender compression factor. This research

introduced the methodology of using these factors to

allow for the generation of a defender placement

strategy aimed at maximizing a visible defender’s

utility to reduce opportunistic crime. The novelty of

this approach allows for application to other large

campuses and living districts to form conclusions

about opportunistic criminal behavior patterns and

formulate an approach to abate such crimes.

ACKNOWLEDGEMENTS

We sincerely thank Dr. Milind Tambe, Dr. Arunesh

Sinha, Chao Zhang, and Dr. Gisele Ragusa for your

very generous support and guidance during this

research project. Your help made this collaboration

successful.

All opinions expressed in this paper are the

authors’ and do not reflect the policies and views of

DHS, USC, or the US Government.

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Hall, R. Classical Conditioning, Psychology World, 1998.

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Nagin, Daniel, et al. Monitoring, motivation and

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Osborne, Martin J., and Ariel Rubinstein. A course in

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Yildiz, Muhamet. 14.12 Game Theory Lecture Notes,

14.12 Economic Applications of Game Theory,

Massachusetts Institute of Technology, 2002.

http://web.mit.edu/14.12/www/02F_lecture3-602.pdf.

Zhang, Chao, Arunesh Sinha, and Milind Tambe.

"Keeping pace with criminals: Designing patrol

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