Crime in Urban Areas: A Data Mining Perspective

Crime in Urban Areas:
                                                                           A Data Mining Perspective

                                                                                   Xiangyu Zhao and Jiliang Tang
                                                                     Data Science and Engineering Lab, Michigan State University
                                                                                    {zhaoxi35,      tangjili}
arXiv:1804.08159v2 [cs.CY] 4 May 2018

                                        ABSTRACT                                                         in place.
                                        Urban safety and security play a crucial role in improving       Traditional urban crime research is mainly based on con-
                                        life quality of citizen and the sustainable development of       ventional demographic data, i.e., statistical socioeconomic
                                        urban. Traditional urban crime research focused on lever-        characteristics of a population, such as education level [36],
                                        aging demographic data, which is insufficient to capture the     income level and wealth gap [59; 75], and ethnic and religious
                                        complexity and dynamics of urban crimes. In the era of big       difference [7]. However, demographic data is insufficient to
                                        data, we have witnessed advanced ways to collect and in-         understand the dynamics and complexity of crimes. First,
                                        tegrate fine-grained urban, mobile, and public service data      most demographic features are relatively stable over an ex-
                                        that contains various crime-related sources as well as rich      tended period of time, which cannot capture the dynamic
                                        environmental and social information. The availability of        nature within a specific community. Second, the vast major-
                                        big urban data provides unprecedented opportunities, which       ity of communities in the urban share similar demographic
                                        enable us to conduct advanced urban crime research. Mean-        features, thus it becomes difficult to capture the differences
                                        while, environmental and social crime theories from crimi-       between different communities [98]. Recently, with the mas-
                                        nology provide better understandings about the behaviors         sive development of new techniques for fine-grained data col-
                                        of offenders and complex patterns of crime in urban. They        lection and integration, numerous urban crime-related data
                                        can not only help bridge the gap from what we have (big          has been recorded, which provides sources that contain help-
                                        urban data) to what we want to understand about urban            ful context information about urban crime. For instance,
                                        crime (urban crime analysis); but also guide us to build         human mobility provides useful environmental factors such
                                        computational models for crime. In this article, we give an      as the function of a region and residential stability, which
                                        overview to key theories from criminology, summarize crime       can significantly impact criminal activities according to en-
                                        analysis on urban data, review state-of-the-art algorithms       vironmental criminology [9]; while meteorological data like
                                        for various types of computational crime tasks and discuss       weather information has been proven to be related to ur-
                                        some appealing research directions that can bring the urban      ban crimes [26; 80]. Thus, big urban data contains rich and
                                        crime research into a new frontier.                              fine-grained context information about when and where the
                                                                                                         data is collected. Such information not only enables us to
                                                                                                         understand the dynamics of crime such as how crime evolves;
                                        1.   INTRODUCTION                                                but also allows us to study crime from various perspectives.
                                        We are living in a rapidly urbanizing world. The United          Hence, big urban data provides us unprecedented opportu-
                                        Nations predicted that by 2050 about 64% of the develop-         nities to conduct advanced investigations on urban crime.
                                        ing world and 86% of the developed world will be urbanized,      On the one hand, there are many criminal theories developed
                                        which means that the urban population will be bigger than        from criminology to explain various types of criminal phe-
                                        the world population today. Nowadays, the relationship be-       nomena. For instance, according to environmental criminol-
                                        tween urbanization and inequalities of urbanites (such as        ogy such as routine activity theory [25] and rational choice
                                        education level and wealth gap) has been extensively stud-       theory [27], crime distribution is highly determined by time
                                        ied [4; 73], and a good amount of research suggests that         and space, and environmental factors offered by human mo-
                                        places with inequalities are more likely to have high crime      bility can significantly affect criminal activities. Meanwhile,
                                        rates [29; 8; 50]. For instance, over the period of 1980 to      social criminology such as social disorganization theory di-
                                        2000, recorded crimes increased from 2300 to 3000 for every      rectly links crime rates to neighborhood ecological charac-
                                        100,000 people [94]. Recent studies have shown that urban        teristics [85], while culture conflict theory suggests that the
                                        safety is closely related to the quality of citizen’s life and   root cause of criminality can be found in a clash of values
                                        the sustainable development of urban [28]. Safety is one         between differently socialized groups over what is acceptable
                                        of the most fundamental physical and psychological needs         or proper behavior. These theories explore many aspects of
                                        of residents. Meanwhile, sustainable urban development           criminal behaviors and are crucial to understand and ex-
                                        will only be achieved when well-planned city-wide, gender-       plain how and why crime occurs. Therefore, they can help
                                        sensitive, community-based, integrated and comprehensive         bridge the gap from what we have (big urban safety data)
                                        urban crime prevention and safety strategies have been put       to what we want to understand about urban crimes (urban
                                                                                                         crime analysis).
                                                                                                         On the other hand, urban data is typically large-scale, noisy,
dynamic and heterogeneous, thus efficient and effective com-      wallet is visible inside a vehicle and no person is around, it
putational solutions are desired. In order to facilitate crime    may tempt a criminal to grasp the opportunity.
research with big urban data, a variety of computational
tasks have been proposed, which have encouraged a large           2.1.4 Awareness Theory
body of computational models by integrating criminal the-         Four components of crime have been suggested in [11]: vic-
ories as well as crime patterns. It is timely and necessary to    tim, criminal, geo-temporal and legal. Concentrating on the
provide an overview about urban crime from a data mining          particular spatial aspect of crime is important to understand
perspective. Then, the remaining of the article is organized      the behavior of criminals. A crime’s space may be chosen
as follows. In Section 2, we introduce environmental and          either deliberately or accidentally by either the victim or the
social criminal theories from criminology. Then we summa-         offender according to their life styles. A number of things
rize the major urban crime patterns in Section 3. In Section      have impact on the crime rate of an region. For example,
4, we introduce key computational crime tasks with repre-         what kind of individuals reside in a particular region and
sentative algorithms. Finally, we conclude the work with          what kind of security can be obtained.
discussions on possible research directions.
                                                                  2.1.5 Broken Windows Theory
2.   CRIMINOLOGY                                                  The broken windows theory is a criminal theory of the norm-
                                                                  setting and signaling impact of urban disorder and vandal-
Crime is a complicated and multidimensional event occur-          ism on extra offense and anti-social behavior [104]. The
ring when the law, offender and target (person or object)         theory claims that sustaining and monitoring urban envi-
converge within time and place [10]. Understanding the of-        ronment to avoid small offenses like public drinking and
fenders’ behavior and crime patterns plays an essential role      vandalism assists to produce an environment of order and
in understanding crime. Consequently, it is beneficial to be      lawfulness, thus preventing more severe offenses happen-
acquainted with the theories from criminology.                    ing.The theory has been applied as an inspiration for many
                                                                  reforms in criminal policy, such as the controversial mass use
2.1 Environmental Criminal Theories                               of “stop, question, and frisk” by the New York City Police
Environmental criminology focuses on criminal patterns within     Department.
particularly built environment and analyzes the impacts of
the external variables on people’s emotional behavior. These      2.1.6 Crime Opportunity Theory
consist of space (geography), time, law, and offender, in ad-     Crime opportunity theory suggests that analysts should search
dition to target or victim.                                       for concentrations of offense targets. For example, a dense
                                                                  downtown community without off-street parking could have
2.1.1 Routine Activity Theory                                     many vehicles parked on the street. This kind of areas might
Routine activity theory explains crime in terms of crime op-      become a region hotspot for thefts from vehicles; while a
portunities that happen in daily life [37; 25]. Three elements    suburban inhabited by dual-income families will have few
should converge in time and space for a crime opportunity,        persons during weekdays, and their property is unprotected,
i.e., a motivated offender, a suitable target or victim, and      thus their community can be a region hotspot of burglary.
the absence of a capable guardian. A guardian at a place,         Note that in such condition, many levels of hotspots can
like a street, could contain security guards or even ordinary     exist simultaneously. Within region hotspots, identified by
pedestrians who would witness the criminal act and possibly       the subdivision in this case, might be streets with increased
intervene or report it to police. This theory is expanded by      amounts of burglaries, and some of the houses on these
the addition of the fourth element of “place manager” who         streets might be broken into numerous times.
has the capacity to take nuisance abatement measures [35].
                                                                  2.2 Social Criminal Theories
2.1.2 Crime Pattern Theory                                        Theories in this family are used in a number of approaches
Crime Pattern Theory is to understand why crimes are com-         as the conflict theory or structural conflict perspective in
mitted in particular areas. Crime is not really random – it is    sociology are associated with crime. Social criminal theories
either planned or opportunistic. Based on the theory, crime       emphasize poverty, absence of education, lack of marketable
happens when the activity space of the victim or target in-       abilities, and subcultural values as fundamental causes of
tersects with that of an offender. Crime Pattern Theory           crime.
has three main notions – node, path and edge [22]. Node
is an specific area of activity that an individual uses fre-      2.2.1 Social Disorganization Theory
quently. Path is the route that the individual takes to and       Social Disorganization Theory directly links crime rates to
from typical areas of activity in everyday life. Edges are the    community environmental characteristics [85]. Social disor-
boundaries of an individual’s awareness space.                    ganization theory postulates that an individual’s residential
                                                                  location is a substantial element shaping the chance the in-
2.1.3 Rational Choice Theory                                      dividual will become involved with illegal activities. The
Rational choice theory aims to help in thinking about situ-       theory shows that, among determinants of an individual’s
ational crime prevention [21]. The assumption is that crime       later illegal activity, residential location is more substantial
is purposive behavior made to fulfill the criminal’s needs for    than the individual’s characteristics (e.g., age, gender, or
things such as money, status and excitement. Meeting these        race). For instance, the theory indicates that youths from
requirements involves the making of decisions and choices as      disadvantaged community participate in a subculture which
these are constrained by limits, ability, and the accessibility   approves of delinquency, and these types of youths thus ac-
of relevant information [23]. For instance, if telephone or       quire criminality within this social and ethnic setting.
2.2.2 Social Strain Theory                                          that labeling theory influenced some youth offenders but not
Strain theory indicates that mainstream culture is saturated        others.
with dreams of opportunity, freedom, and prosperity. The
majority of people buy into this dream, and it will become a        3. URBAN CRIME PATTERN ANALYSIS
powerful cultural and psychological inspiration. If the social      As suggested by theories from criminology, crime is highly
structure of opportunities is unequal and prevents the ma-          related to time and location. Meanwhile, big urban data
jority from realizing the dream, some of the people dejected        provides rich information about crime from temporal and
will use illegal ways (crime) to realize it. Others may retreat     spatial perspectives, which cultivated increasing efforts on
or drop out into deviant subcultures (like gang members).           temporal-spatial pattern analysis. Temporal-spatial pat-
Robert Agnew developed this theory to incorporate varieties         tern analysis is a procedure that obtains understanding from
of strain which were not derived from economic restrictions.        temporal-spatial related sources and generates understand-
This is known as “General Strain Theory” [68].                      ing for crime analysts. In practice, understanding varies
                                                                    among different environments. In order to acquire appropri-
2.2.3 Culture Conflict Theory                                       ate relevant kinds of information, various kinds of temporal-
The theory of culture conflict is linked to the disagreement        spatial pattern analysis techniques should be leveraged [63].
over dissimilarities in values and beliefs. This is based on
the idea that different cultures or classes cannot agree on         3.1 Temporal Pattern Analysis
what is common acceptable behavior. For instance, if the            Criminal temporal patterns are complicated since temporal
upper and middle classes work to make a living in a legal           resources could be structured in various intervals like weeks,
way, others may use illegitimate ways, such as stealing, to         months, seasons, years and others [63]. Generally, the tem-
make a living.                                                      poral crime analysis focuses on learning useful temporal pat-
                                                                    terns from sequential crime data. Types of temporal pattern
2.2.4 Social Efficacy Theory                                        analysis can be summarized as follows:
Recent evidence points to the role of social efficacy, which is
the willingness of nearby residents to intervene with regard           • Crime tendency refers to the change of a type of crime
to the common good. This is dependent on mutual trust and                inside a given region and a long-term time period. For
solidarity among neighbors [83]. Communities that have a                 example, the property crime rates declined by double-
great deal of social efficacy have less offenses than these at           digit percentages from 2008 to 2016 in the USA.
low levels. Social efficacy is not a property of individual
                                                                       • Crime periodicity is defined as the repeating patterns
people or places, but a characteristic associated with groups
                                                                         of crime at time intervals, e.g., seasonal (i.e. annually
of individuals.
                                                                         recurring) crime patterns.
2.2.5 Subcultural Theory                                               • Similarity search of crime aims to search crime se-
Subcultural theorists focus on small cultural groups frag-               quences that are similar to a given crime sequence.
menting aside from the mainstream that form their own
beliefs and meanings of life. It indicates that delinquency            • Sequential behavior analysis tries to find an offender’s
among lower class youths is a reaction towards the social                sequential behaviors before or after committing a crime,
norms of the middle class [24]. Several youth, especially                e.g., a burglar often buys drug after committing a bur-
from poorer regions where opportunities are few, might buy               glary.
into social norms specific to those places that may consist
of “toughness” and disrespect regarding authority. Criminal         3.2 Spatial Pattern Analysis
acts might result when youths adapt to norms of the deviant         Crimes are not evenly or randomly distributed in an urban
subculture [61].                                                    area. Typically, crimes are dense in some regions and sparse
                                                                    in others. Spatial pattern analysis aims to learn the aggre-
2.2.6 Control Theory                                                gation of crime, i.e., hotspots, inside a city. Additionally,
Control Theory tries to describe why people do not become           crimes are proved to be correlated with environment con-
offender [49]. It recognizes four principal factors: (1) connec-    texts. In this subsection, we introduce crime hotspots and
tion to others, (2) belief in ethical validity of principles, (3)   spatial factor analysis in detail.
responsibility to achievement, and (4) engagement in main-             • Crime hotspot is defined as a geographic location with
stream activities [54]. The more an individual has those                 more than normal quantity of crime activities, or a
factors, the less likely he/she become offender. This theory             location where individuals have greater than normal
is extended with the fact that an individual with low self               risk of victimization [34]. On the contrary, there exist
control is more likely to become offender.                               cold-spots with less than the normal density of crime.
                                                                         Some hotspots might be hotter than others because
2.2.7 Labeling Theory
                                                                         of the difference of crime density. Generally, hotspot
Labeling theory claims that when a person is given the label             analysis finds spatial patterns through spatial cluster-
of a offender, they might accept it and continue to commit               ing.
crime or refuse it. Even those who initially refuse the label
can eventually accept it as the label becomes more well-               • Spatial factor analysis aims to find the main spatial
known especially among their peers. This stigma can be                   factors of crime [63]. The major hypothesis of spa-
much more profound when the labels are about deviancy,                   tial analysis is that crime should correlate with en-
and it is believed that this stigmatization can cause de-                vironment contexts and this hypothesis is supported
viancy amplification. Klein [60] did a test which indicated              by various criminal theories. For instance, according
to routine activity theory, three elements, i.e., a mo-      that average offense number must be lager than 30 to ob-
       tivated offender, a suitable target or victim, and the       tain less than 20% prediction error. It is also found that
       absence of a capable guardian, are required to converge      Holt exponential smoothing is the most precise model for
       in time and space for a crime occurring.                     precinct-level crime prediction. In [17], autoregressive inte-
                                                                    grated moving average (ARIMA) is employed for near fu-
3.3 Spatio-Temporal Pattern Analysis                                ture prediction of property crime. Based on 50 weeks’ prop-
Criminal spatio-temporal pattern analysis aims to obtain            erty crime data, an ARIMA model is built to predict crime
understanding from geo- and time-related crime data. The            number of 1 week ahead. It is found that ARIMA model
challenge is how to identify patterns from the dynamic inter-       has higher fitting and prediction precision than exponential
action among space, time and crime [63] since crime patterns        smoothing.
are believed to vary with time and location [89; 66; 51]. In        A four-order tensor for crime forecasting is presented in [71].
this subsection, we will review important temporal-spatial          The tensor encodes the longitude, latitude, time, and other
patterns of urban crime.                                            related crimes. The tensor can tackle the data sparsity since
                                                                    each order is lower-dimensional. Additionally, the geometry
     • Earthquake-like pattern: The concentrating patterns
                                                                    structure is properly maintained in tensor. Leveraging the
       suggest that an earthquake is likely to produce a series
                                                                    tensor framework, empirical discriminative tensor analysis
       of aftershocks close to the area of the original earth-
                                                                    algorithm is presented to acquire adequate discriminative in-
       quake [33]. Similar phenomena are observed in crime
                                                                    formation and reduce empirical risk simultaneously. In [107],
       formation, such as burglars may repeatedly assault
                                                                    a new feature selection and construction method is proposed
       neighboring communities over a time period. This
                                                                    for crime prediction by using temporal and spatial patterns.
       encourages applying seismology techniques like self-
                                                                    Multi-dimensional feature is denoted as spatio-temporal pat-
       exciting point processes to model urban crime [30].
                                                                    tern that is built upon regional crime cluster distributions in
     • Spatio-temporal hotspot : Crimes such as gang vio-           different levels. Then a Cluster-Confidence-Rate-Boosting
       lence happen concentrated in time and space. Spatio-         framework is presented to combine local spatio-temporal
       temporal hotspot is defined as a geographic location         patterns into global crime pattern, which is then employed
       coupled with a time period where greater than normal         for crime prediction.
       amount of crimes occur. It aims to incorporate tem-          Temporal patterns of dynamics of violence are analyzed us-
       poral patterns on spatial hotspot for crime analysis.        ing a point process model in the scenario of urban crime
                                                                    prediction [65] . The rate of crimes is partitioned into the
     • Spatio-temporal correlations: Spatio-temporal corre-         sum of a Poisson background rate and a self-exciting com-
       lations are explored in [113]. For a urban region, “intra-   ponent in which crimes induce the growth in the rate of
       region temporal correlation” is observed– (i) for two
                                                                    the process. Specifically, each crime produced by the pro-
       consecutive time slots, they are likely to share similar     cess in turn produces a series of offspring crimes according
       crime numbers; and (ii) with the increase of differences     to a Poisson distribution. The background rate is normally
       between two time slots, the crime difference has the         fixed for crimes. In [69], self-exciting point process mod-
       propensity to increase. Over all urban regions, “inter-      els are implemented for predicting crimes. They leverage a
       region spatial correlation” is observed – (i) two geo-       nonparametric evaluation strategy to gain understanding of
       graphically close regions have similar crime numbers;
                                                                    temporal-spatial triggering function and temporal tenden-
       and (ii) with the increase of spatial distance between       cies in the background rate of burglary. Particularly, spatial
       two regions, the crime difference tends to increase.         heterogeneity in crime rates can be evaluated by background
                                                                    intensity estimation and the self-exciting effects detected in
4.     COMPUTATIONAL TASKS FOR URBAN                                crime data.
Big urban data is typically large-scale, noisy, dynamic and         4.1.2 Prediction Based on Environmental Context Data
heterogeneous, which calls for efficient and effective compu-       Crime rate tendencies and periodicity are analyzed through
tational solutions. Thus, in order to enhance crime research        a routine activity approach [25; 38] to predict crime. Specif-
in big urban data era, numerous computational tasks have            ically, it is assumed that the distribution of events far from
been proposed. In this section, we review key computational         homes raises the opportunities for offense and hence yields
tasks for urban crime with representative algorithms.               higher crime rates. The assumption can help understand
                                                                    crime rate tendencies in the United States 1947-1974 as a
4.1 Crime Rate Prediction                                           consequence of changes in such factors as labor force in-
Crime rate prediction aims to predict the future crime rate         volvement and single-parent families. Seasonal crime pat-
of a given urban region. In this subsection, we categorize          terns were analyzed for urban crime prediction [40]. An
crime rate prediction models according to the data they use         evaluation of annual, quarterly, and monthly crime data ex-
as prediction based on crime data, environmental context            hibited solid evidence that temperature has a positive im-
data, andmsocial media data.                                        pact on most kinds of crime. The influence was independent
                                                                    with seasonal variation. The key explanation is that higher
4.1.1 Prediction Based on Crime Data                                temperatures trigger individuals to spend more time out of
Precise crime prediction 30 days ahead for small areas, like        home, which is consistent with routine activity explanations
police precincts, is proposed in [48]. Prediction precision         for crime and has been revealed to raise the chance of crime.
of univariate time series models are compared with tech-            The results indicate that temperature is one major reason
niques commonly employed by police. A fixed-effect re-              to be taken into consideration when describing quarter-to-
gression model of absolute percent prediction error suggests        quarter variations of urban crime.
4.1.3 Prediction Based on Social Media Data                       eters of KDE such as the grid cell size and search radius
Twitter posts with rich and event-based context is lever-         (bandwidth) are proposed for hotspot detection tasks [14;
aged for predicting criminal incidents [100]. The frame-          34; 82].
work contains two components. The first component is a
spatio-temporal generalized additive model, which leverages       4.2.2 Reaction-Diffusion-based Techniques
a feature-based method to predict future crime at a given         A computational framework based on reaction-diffusion par-
location and time. The second component extracts tex-             tially differential equations is developed for studying the for-
tual information through semantic role labeling-based la-         mation and dynamics of crime hotspots [87]. The framework
tent Dirichlet allocation. In addition, a new feature se-         is designed upon empirical evidence for how criminals move
lection approach is designed to discover essential features.      and interact with victims. Analysis suggests that crime
A preliminary analysis of Twitter-based crime prediction is       hotspots from the recurring crimes diffuses locally, but not
proposed in [101]. The method incorporates intelligent se-        so far as to mix remote crime together. A nonlinear anal-
mantic analysis of Twitter posts, and dimensionality reduc-       ysis is proposed to detect the crime hotspots through the
tion through latent Dirichlet allocation. Twitter-specific lin-   reaction-diffusion system [86]. The authors discover ampli-
guistic analysis and mathematical topic modeling to locate        tude equations that control the forming process of crime
discussion topics of Twitter across a urban are introduced        hotspot patterns through a perturbation method. Differ-
in [45]. These topics are integrated into a crime predic-         ent from the super-critical hotspots discovered in existing
tion model. The authors find that the addition of Twitter         work [87], sub-critical hotspots are discovered that arise
information enhances crime prediction accuracy compared           upon sub-critical or trans-critical bifurcations with respect
with kernel density estimation. It identifies several perfor-     to the geometry. Enlightened by [86], a reaction-diffusion
mance bottlenecks that influence the usage of Twitter in          based approach is proposed to detect hotspots rigorously [5].
a real decision support system. In [1], Twitter content is        More specifically, the existence of steady states is demon-
employed for crime tendency forecast, in which a Twitter          strated with multiple spikes of two types, i.e., (1) Multiple
sampling approach is presented to gather historical data for      spikes having the same amplitude, and (2) Multiple spikes
handling the missing data problem over time. The experi-          having different amplitudes. They leverage a strategy ac-
ments unveiled the relationship of Twitter content and crime      cording to Liapunov-Schmidt reduction and improve it to
tendency. Besides, some crime types like burglary are found       the quasilinear crime hotspot model.
to have closer relationship with the shared Twitter content
than other types.                                                 4.2.3 Other Techniques
                                                                  Geographic boundary thematic mapping is a method to rep-
4.2 Crime Hotspot Detection                                       resent spatial distributions of urban crimes [81], which can
Crime hotspot detection (mapping) is a spatial mapping            rapidly generate hotspot maps and need little knowledge to
technique focusing on the identification of the concentra-        interpret [103]. Boundary regions in this method are gener-
tion of crime events across the urban. In this subsection, we     ally arbitrarily defined by government, e.g., police precinct.
categorize crime hotspot detection methods based on the           Crimes in the hotspot map concentrate on these regions
types of techniques they leverage, i.e., (1) KDE-based tech-      which will then be shaded with respect to crime number
niques: a non-parametric method to calculate the probabil-        inside them. Grid thematic mapping method is developed
ity density function of crimes, (2)Reaction-Diffusion-based       to mitigate the situation of different sizes and shapes of dif-
techniques: a mathematical framework based on reaction-           ferent regions such as police precincts [6; 62], in which grids
diffusion partial differential equations to learn the dynamic     with the same size and shape are drawn on a urban map
nature of crime hotspots, and (3) Other techniques: they          snapping the study area. Thus all regions in the map are
include geographic boundary thematic mapping, grid the-           of uniform dimensions and are comparable, which is helpful
matic mapping, spatial ellipses and hotspots optimization         to quickly and easily detect crime hotspots. Spatial ellipses
tools.                                                            is a hotspot detection software that locates hotspot within
                                                                  the study area [3]. It first finds the densest aggregation of
4.2.1 KDE-based Techniques                                        crime locations on the map (hot clusters), and then fits a
Prospective crime hotspot detection methods are improved          “standard deviation-ellipse” to each one. The ellipses rank
by analyzing interpolation technique, grid cell size, and band-   crime clusters according to their sizes and properties. An
width on the prediction precision of Kernel Density Estima-       hotspots optimization tool is presented to enhance the de-
tion (KDE) [52]. Particularly, based on variations in es-         tection of hotspots through optimizing its boundary accord-
sential user-defined settings that are parts of the interpo-      ing to the spatial patterns of crime driving factors in [97;
lation process, this work presents scientific explanations of     96]. A pattern is introduced to indicate a mix of values of
the quality of KDE hotspot maps . The analytical technique        related variables which is able to distinguish hotspots and
contains evaluating these effects across multiple crime types,    normal regions from the spatial perspective, named Geospa-
such as assault, robbery and burglary. To quickly get an ac-      tial Discriminative Patterns (GDPatterns) [32]. The pro-
curate hotspot map, an efficient approach to convert KDE          posed model automatically detects the crime hotspots and
hotspot map with low resolution to a new map with con-            identifies GDPatterns between crime hotspots and normal
tour lines is designed in [31]. The outcome is a hotspot map      regions simultaneously.
with smooth boundaries, which is equally accurate to KDE
hotspot maps leveraging smaller cell sizes, but has faster        4.3 Next-Location Prediction
generation speed. The new maps are more natural illustra-         Next-Location Prediction aims to predict the location where
tion of the real world’s hotspots compared to the original        an offender will commit a crime according to the offender’s
KDE maps. Many helpful suggestions for setting param-             historical trajectories or other information. A personalized
random walk based method for next-location prediction is          have red or blue association but are otherwise indistinguish-
proposed in [91]. To be specific, it leverages co-offending,      able. In this model, all indirect interplays happen through
crime trends and road network data to personalize the ran-        graffiti marks, on-site and on closest surrounding regions.
dom walk process. According to crime pattern theory, crim-        The dynamic segregation [84] and dynamic subsequent vari-
inals usually use their most familiar regions as part of their    ations [41; 67] models leverage agent-based techniques with
activity space. A probabilistic model is proposed to cap-         structured time-invariable interactions [77] for criminal net-
ture known criminals’ spatial trajectories in their activity      work analysis. They use structured rather than well-mixed
space. This setting is then used to predict crime locations       networks since not all actors are connected to others in a
for criminals. Correlated walk analysis with several regres-      gang or criminal network, and the interplays between actors
sion routines are designed for forecasting the behavior of        generally follow an fixed manner that will not change over
a serial criminal in [64]. Based on the analysis of crimi-        time.
nal’s repeated behavior in time, direction, and distance, the
prediction of where and when the next crime will occur is         4.4.2 Graph Theory-based Techniques
produced. In [99], approaches that incorporate textual con-       Analytical Hierarchy Process and Graph Theory are com-
tent into next-location prediction models are studied based       bined to solve gang crime problem [44]. The key purpose is
on two hypothesis: (1) An person’s future spatial trajectory      to find the conspirators and produce a priority list according
relates to his/her historical tweets, and (2) Crime rates cor-    to message traffic within crime cases. To find one offender,
relate with the density of users’ spatial trajectories in the     it firstly quantifies the topics through Analytic Hierarchy
same region. Additionally, the relationship between these         Process, then builds the network model through Graph The-
next-location predictions and the incidence of urban crimes       ory and finally proves the relationship between this offender
is investigated, with the target to help future study into        to the identified conspirators and non-conspirators. Crim-
intelligent crime prediction. In [79], Rossmo’s formula is in-    inal gangs are sensed and characterized in networks recon-
troduced to predict crime’s next location with geographic         structed from telephone network data [39]. Specifically, it
profiling techniques. To be specific, a traffic network is in-    presents an expert framework to reveal the main structure of
corporated for geographic profiling, and the next-location        criminal networks concealed in telephone data. This frame-
prediction problem is handled upon weighted traffic net-          work enables mathematical network analysis and community
work, where shortest path between nodes are leveraged to          detection of telephone network data. It allows police depart-
replace Euclidean distance for accurate next crime location       ments to deeply understand the structure within criminal
prediction. An agent-based simulation is designed to learn        networks, discover offender leader and identify relationship
the influence of temporal pulse activities on the criminal        among sub-groups. In [76], several police analytic tasks are
location selection process [42]. The simulation offers a tech-    handled regarding street gangs from the graph theory per-
nique to modify spatio-temporal patterns as the consequence       spective. Particularly, it establishes the degree of member-
of some apriori special activities.                               ship for criminals who do not acknowledge the membership
                                                                  in a street gang, quickly recognizes sets of influential crimi-
4.4 Criminal Network Analysis                                     nals through the tipping model, and decomposes gangs into
Law enforcement and police departments have realized that         sub-gangs to identify criminal ecosystems. A unified model
criminal networks are important for crime analysis and pre-       is proposed to bridge the conceptual gap between abstract
vention. Typically, a criminal network consists of (1) nodes:     crime dataset and co-offending network in [90]. Then it
the individual actors within the criminal network such as         uses several centrality metrics, such as degree, closeness,
offenders, and (2) ties: the relationships between actors,        betweenness, eigenvector and PageRank centrality, on the
such as co-offenders and crime gang. In this subsection, we       co-offending network and studies how leader criminal de-
categorize criminal network analysis methods according to         tection and elimination can help crime prevention. Cluster
the techniques they employ as (1) Agent-based techniques:         analysis is applied to detect criminal leaders, gangs and in-
agents move in network and interact with each other, thus         terplays between gangs within criminal network [105]. More
produce complex dynamics and patterns from simple be-             specifically, an concept space idea is introduced to build links
havioral rules, (2) Graph Theory-based techniques: Metrics        among criminals according to the similarities of criminals’
(e.g. centrality) and techniques (e.g. community detection)       crime activities. The more two criminals take part in the
from graph theory are employed for criminal network analy-        same crime activities, the more likely to have a link between
sis, and (3) GIS-based techniques: Geographic Information         two criminals.
System techniques are introduced to handle criminal net-
work analysis.                                                    4.4.3 GIS-based Techniques
                                                                  Influence of geography and social networks on gang violence
4.4.1 Agent-based Techniques                                      is learned in [74]. Applying urban shootings data, it analyzes
An agent-based model to imitate the formation of street           the impact of geographic proximity, organizational memory
gangs is introduced in [53]. The motion dynamics of agents        and group properties (e.g. reciprocity and transitivity) on
are combined into an evolving network of street gangs, which      gang violence in Chicago and Boston. Results show ad-
are influenced by prior interplays among agents in the sys-       jacency of criminal gang turf and previous conflict between
tem. Datasets of gangs, locations and criminal behaviors          gangs are solid predictors of future gang violence. A method
are incorporated into the model. The authors discover that        for co-offense forecast is proposed in [92], where geographic,
highways, rivers, and the center locations of gangs’ activities   social, geo-social and similarity factors are used to classify
affect the agents’ motions. The gang concentration through        offenders. To handle the skewed distribution problem of co-
an interacting agent system is identified on a lattice [2] .      offending networks, it designs three types of criminal coop-
Two-gang Hamiltonian framework is presented that agents           eration opportunities which are helpful to reduce the class
imbalance ratio, while maintaining half of the co-offenses.      of random activities, the likelihood of which changes once
Criminal network among gang members are discovered in            an crime occurs. Near repeat and social network techniques
Los Angeles according to the rare observations of a mix of       are incorporated on discovering crimes’ spatio-temporal pat-
social connections and geographic regions of the individu-       terns [55], in which burglary data of NYC is analyzed and
als [95]. A similarity graph is built for the individuals and    compared upon average clustering coefficient, degree and
spectral clustering is leveraged to identify clusters in the     closeness centrality. The clusters of near repeat crimes are
graph. It analyzes various ways to encode the geo-social         efficiently calculated in [106]. First, R-tree is used to index
information on graph structure and the effect on the result-     crimes, where a crime is defined as a node and edges are
ing clusterings. Spatial and social distance are employed        built by range querying the vertex in R-tree, thus a graph
to study the connections in youth co-offending network and       forms. Cohesive subgraph techniques are used to find the
essential features that influence co-offending network forma-    crime chains. K-clique, k-truss, k-core plus DBSCAN algo-
tion. Results demonstrate that spatial distance can better       rithms are implemented in sequence regarding their diverse
describe the overall structure, and social distance plays a      range of capacity to locate cohesive subgraphs.
role in network structure of close spatial distance.
                                                                 4.6 Police Patrolling
4.5 Near Repeat Victimization                                    Proper patrol route planning is one important application
Crime does not happen randomly or evenly across time or          of crime analysis systems, which helps increase the effective-
space. The near-repeat victimization identifies the increased    ness of police patrolling and improve public security simul-
risk of repeat victimization at the same or surrounding re-      taneously. In this subsection, we categorize this family of
gions and within a certain time period. This phenomenon          models according to the application tasks including (1)Pa-
has been repeatedly demonstrated for urban crime over the        trol Area Allocation: partitioning a urban to precincts and
world. Near-repeat phenomenon is often jointly analyzed          arranging them to police officers, (2)Patrol Route Planning:
with hotspot detection tasks because their similar spatio-       designing the patrolling route for police car, and (3) Other
temporal distributions, but there are also some other tech-      Applications: they include police decision support systems,
niques to handle near-repeat victimization, such as social       and spatial reorganization of police agents.
network analysis.
                                                                 4.6.1 Patrol Area Allocation
4.5.1 Hotspots-based Techniques                                  A novel framework is designed for allocating patrol area
Time span of repeat victimization and relationships between      against urban crime [46; 109; 108]. This framework models
repeat victimization, deprivation and burglary hotspots are      the connection between officers and urban crime as a dy-
studied in [56]. It finds that the time span of repeat victim-   namic Bayesian Network (DBN). Next, a series of improve-
ization presents an exponential manner. Results also reveal      ments are made to the basic DBN causing in a compact
a clear connection between repeat victimization and depri-       model that has lower learning error. Further, by analyz-
vation, and declare that the geographical area of repeat vic-    ing various Markov models, it is found that the number of
timizations may well contribute to the definition of burglary    the crime and the number of the defender in each region
hotspots. Encouraged by the precepts of optimal foraging         can impact the crime forecast, and combining hidden states
theory, burglary hotspots are found to shift over time [57],     within DBN can reduce prediction error. A bi-level opti-
such that the repeating phenomenon of hotspots is not pre-       mization method are developed to handle the problem of
dictable over three months, but they have a tendency to          spatial police patrol allocation aiming to enhance crime re-
move in a slippery way, i.e., moving to surrounding regions      sponse speed [72]. It first designs a linear programming pa-
at successive time slots. Repeating burglary is studied based    trol response formulation and then use Bender’s decomposi-
on police calls for service data [93]. It demonstrates: (1)      tion to solve the optimization problem. The major challenge
hotspots can be discovered by mathematical analysis of spa-      is that offenders may adjust the location and time of crime
tial crime aggregation, (2) unstable hotspots are generally      with respect to police patrols. To deal with this challenge,
short-term concentrations of hot-dots, while stable hotspots     an iterative Bender’s decomposition approach is proposed.
appear to reveal more social and physical features of specific   In [112], a police patrol discrete-event simulation model is
locations. In [102], the near-repeat phenomenon is used to       applied to judge the patrol allocation plans. A response sur-
analyze the risk levels around hotspots. To be specific, a       face strategy is developed to discover optimal or sub-optimal
temporal matrix is proposed to measure the fluctuation of        allocation plans to improve response speed and reduce work-
risk around hotspots. The results show that (1) hotspots al-     load variation. An iterative searching process is designed to
ways exist, (2) space-time regions of high chance are always     learn the connection between parameters in a redistricting
variable in space and time, (3) locations in the vicinity of     algorithm and performance measures of allocation plans.
hotspots concurrently share higher risk, and (4) crime risks
around hotspots follow a wave diffusion process.                 4.6.2 Patrol Route Planning
                                                                 Planning effective and balanced routes for police patrolling
4.5.2 Other Techniques                                           is challenging with multiple police cars across different police
Likelihood distribution functions for the time intervals be-     distinct. Distributed services on road networks are intro-
tween repeat crimes are learned in [88]. It compares these       duced for patrolling route planning [16]. Specifically, they
distributions to mathematically derived distributions where      formulate this problem as a Min-Max Multiple-Depot Rural
the repeat effects are due to solely consistent risk hetero-     Postman Problem. To resolve the routing problem, they de-
geneity. It discovers that a form of event boosts is able to     sign an effective tabu-search-based algorithm and present
describe the observed distributions, while risk heterogeneity    three novel lower bounds to evaluate the routes. Rapid
alone cannot, thus it models repeat victimization as a series    route planning is coupled with interactive spatio-temporal
hotspot exploration in [47] . The major components are: (1)         many urban computing tasks such as traffic flow forecast-
a sketch-based method for dynamic route planning, which             ing [110; 111], and air quality prediction [78]. Therefore,
allows a police officer to fast establish a route across the city   one promising direction is to build novel models such as deep
and discover the number and types of crime along the route,         learning models to learn more complex spatio-temporal pat-
and (2) a spatio-temporal hotspot method considering time,          terns for advancing urban crime analysis.
location, season, and recent crime volume. A patrol routes
planning method is designed to maximize the coverage of             5.2 More Advanced Techniques
hotspots and minimize the patrolling distance simultane-            Urban crime is intrinsically complex because of its dynamic
ously [15]. It treats the road network as graph, where node,        interplay with space, time and other factors like economics,
edges and edge weights refer to intersections, streets and          environment and urban configuration. Thus more advanced
streets’ importance. These features as well as the topology         techniques should be introduced and developed to handle
of graph are then used to calculate the optimal patrol route.       crime analysis. For instance, deep reinforcement learning,
This method allows the automation of patrol planning and            which can continuously update polices during the interac-
the dynamic adjustment in terms of constantly changing en-          tions with environment, is suitable for capturing the dy-
vironment. A real-time patrol route planning approach for           namic nature of urban crime data. Besides, crime in ur-
dynamic environments is proposed in [19; 18]. It first models       ban is impacted by multiple sources such as meteorological
the route planning problem in one patrol unit case. Then it         data, point of interests (POIs) data and human mobility
designs an efficient algorithm to leverage cross entropy for        data [113]. The majority of existing algorithms handle mul-
real-time applications in practice. A graph-based MDP is            tiple sources equally or in a linear manner, but fail to cap-
presented to model the patrol routing process in [20], and          ture the nonlinear connections and subordinations among
then it proposes an ǫ-optimal strategy to handle the dimen-         multiple sources [58]. This calls for advanced techniques
sionality curse problem. This strategy is derived from the          to effectively incorporate features from multiple sources for
idea of ǫ-optimal horizon approximation.                            crime analysis. Additionally, feature extraction from mul-
                                                                    tiple sources should follow an automatic way since hand-
4.6.3 Other Applications                                            crafted features are insufficient to capture complex spatio-
A decision support system, which merges predictive polic-           temporal patterns, which encourages to leverage End-to-
ing abilities with a patrolling districting model, is proposed      End frameworks to automatically combine feature extrac-
for the planning of predictive patrolling regions [12]. The         tion and computational tasks of urban crime.
system efficiently and evenly identifies partitions of a dis-
trict balanced based on the decision maker’s preferences. To        5.3 More Computational Tasks
analyze the crime records, it designs a method to describe          The recent development of big data techniques has greatly
the spatially and temporally indeterminate crime events.            advanced urban crime analysis, which provides unprecedented
A multi-criteria police districting problem is studied with         and unique opportunities to designs more sophisticated mod-
the consideration of the characteristics of region, risk, com-      els to tackle practical policing tasks in real world. As an
pactness, and mutual support [13]. The decision-maker can           example, the stop-question-and-frisk program in New York
identify its preferences on the characteristics, workload bal-      City is a crime prevention policy that temporarily detains,
ance, and efficiency. The model is resolved in the form of          questions and searchs citizens on the street for weapons and
a heuristic algorithm. In [43], an application is proposed          contraband. However, this practice has been complained
for assisting the spatial reorganization of police agents. To       about its racism and failure to reduce crime such as bur-
model activities of criminals, it employs self-organization         glary and robbery. Thus more efforts should be made on
strategy where police agents learn from their local regional,       crime prevention strategies that maximize deterrent value
and make decisions based on this self-organization strategy         and minimize infringement on the rights of citizens simulta-
and other environmental information. Two models to help             neously. Besides, multiple urban tasks should be jointly con-
police department design policy and prevention strategies           sidered for a safer and smarter city such as education, health,
against crimes are introduced in [70]. The first model de-          urban planning, economic development, employment, police,
velops a patrol dispatch strategy where police agents patrol        justice, immigration, poverty, integration, etc.
separately without the knowledge of other agents’ locations,
while in the second strategy, the patrols of police agents are      5.4 Urban Simulation
jointly dispatched.                                                 Policing strategies must be pre-evaluated before their active
                                                                    use in order to save the unnecessary cost of deployment and
5.   FUTURE RESEARCH DIRECTIONS                                     avoid negative impacts on urban safety. Thus, a urban en-
                                                                    vironment simulation is necessary for the offline evaluation
In this section, we discuss some insights and present some
                                                                    and visualization of new policing strategies. Moreover, ur-
future directions.
                                                                    ban environment simulation can allow researchers and police
5.1 More Crime Pattens                                              department to investigate, gain insights, and develop polic-
                                                                    ing techniques to boost their communities, integrating the
Urban crime is observed to have intrinsically complex spatio-
                                                                    interplays between crimes, economy, and urban configura-
temporal patterns with complicated urban configurations.
However, the majority of existing algorithms can capture
only certain aspects of patterns. Hence, comprehensive tech-
niques are desired to learn complicated temporal-spatial pat-       6. CONCLUSION
terns for urban crime analysis. Recently deep learning has          Crime analysis plays a tremendously impactful role in the
been demonstrated in the capability of capturing complex            sustainable development of urban and the quality of citizen’s
spatio-temporal patterns for more accurate prediction in            life. With recent advances in urban data sensing, collecting
and integrating technologies, a large amount of fine-grained        [13] M. Camacho-Collados, F. Liberatore, and J. M. An-
urban crime-related data has been recorded with rich envi-               gulo. A multi-criteria police districting problem for the
ronmental and social information, which motivates a variety              efficient and effective design of patrol sector. Euro-
of computational tasks to advance urban crime analysis. In               pean Journal of Operational Research, 246(2):674–684,
this article, we give an overview about urban crime from a               2015.
computational perspective. We first review two families of
criminal theories, i.e., environmental criminal theories and        [14] S. Chainey and J. Ratcliffe. GIS and crime mapping.
social criminal theories, and then key crime patterns in min-            John Wiley & Sons, 2013.
ing urban crime data. We introduce major computational
urban crime tasks with representative algorithms. We also           [15] S. S. Chawathe. Organizing hot-spot police patrol
discuss some interesting research directions about computa-              routes. In Intelligence and Security Informatics, 2007
tional crime with big urban data.                                        IEEE, pages 79–86. IEEE, 2007.

                                                                    [16] H. Chen, T. Cheng, and J. Shawe-Taylor. A balanced
Acknowledgements                                                         route design for min-max multiple-depot rural post-
This research is supported by the National Science Founda-               man problem (mmmdrpp): a police patrolling case. In-
tion (NSF) under grant number IIS-1714741 and IIS-1715940.               ternational Journal of Geographical Information Sci-
                                                                         ence, 32(1):169–190, 2018.
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