Filtering Estimated Crime Series Based on Route Calculations on Spatio-temporal Data

Abstract

Law enforcement agencies strive to link serial crimes, most preferably based on physical evidence, such as DNA or fingerprints, in order to solve criminal cases more efficiently. However, physical evidence is more common at crime scenes in some crime categories than others. For crime categories with relative low occurrence of physical evidence it could instead be possible to link related crimes using soft evidence based on the perpetrators' modus operandi (MO). However, crime linkage based on soft evidence is associated with considerably higher error-rates, i.e. crimes being incorrectly linked. In this study, we investigate the possibility of filtering erroneous crime links based on travel time between crimes using web-based direction services, more specifically Google maps. A filtering method has been designed, implemented and evaluated using two data sets of residential burglaries, one with known links between crimes, and one with estimated links based on soft evidence. The results show that the proposed route-based filtering method removed 79 % more erroneous crimes than the state-of-the-art method relying on Euclidean straight-line routes. Further, by analyzing travel times between crimes in known series it is indicated that burglars on average have up to 15 minutes for carrying out the actual burglary event.

Full text

Filtering Estimated Crime Series Based on Route
Calculations on Spatio-temporal Data
Martin Boldt and Jaswanth Bala
Department of Computer Science and Engineering
Blekinge Institute of Technology
SE-371 79 Karlskrona, Sweden
martin.boldt@bth.se, jaswanthc52@gmail.com
Abstract—Law enforcement agencies strive to link serial
crimes, most preferably based on physical evidence, such as
DNA or fingerprints, in order to solve criminal cases more
efficiently. However, physical evidence is more common at
crime scenes in some crime categories than others. For
crime categories with relative low occurrence of physical
evidence it could instead be possible to link related crimes
using soft evidence based on the perpetrators’ modus
operandi (MO). However, crime linkage based on soft
evidence is associated with considerably higher error-
rates, i.e. crimes being incorrectly linked. In this study,
we investigate the possibility of filtering erroneous crime
links based on travel time between crimes using web-based
direction services, such as Google maps. A filtering method
has been designed, implemented and evaluated using two
data sets of residential burglaries, one with known links
between crimes, and one with estimated links based on
soft evidence. The implementation was verified on the
data set with known linked crimes as the method did
not filter out any of these crimes. Next, the route-based
filtering method was compared to a traditional Euclidean
straight-line-based filtering method. The results show that
the proposed route-based filtering method removed 79 %
more erroneous crimes than the state-of-the-art method.
Roughly 4 % of the crimes linked by the use of soft
evidence could be filtered using the proposed method.
Further, by analyzing travel times between crimes in
known series it is indicated that burglars on average have
up to 15 minutes for carrying out the actual burglary
event.
I. INTRODUCTION
For crime categories that involve serial offenders, i.e.
where the offender commits two or more crimes of
same type, law enforcement agencies strive to combine
crimes committed by the same offender(s) into crime
series [9][16]. This allows investigators to get a more
complete picture based on all information and evidence
collected from the various crime scenes, compared to
investigating each crime in isolation [18]. Also, the
construction of crimes into series has proved to be
more resource efficient than investigating each crime
individually, given that the crimes in the series really are
committed by the same offender(s) [16]. Linking crimes
into series could be done based on physical evidence,
e.g. DNA or fingerprints, but such evidence may not
be present at every crime scene and could be more
frequent for crimes in some crime categories than in
others [18][10]. Additionally, the processing of phys-
ical evidence can be both time-consuming and costly,
making it unfeasible for some agencies to handle large
numbers of physical evidence from high-volume crime
categories [17]. For crime categories where physical
evidence is not available it is instead possible to rely on
soft evidence based on the perpetrators’ modus operandi
(MO) and behavioral patterns manifested at the crime
scene using for instance psychological and geographic
profiling [1][21]. In this paper we refer to such crime
links as estimated links, and the series they constitute as
estimated series.
Compared to links based on physical evidence, esti-
mated links are not as robust since they lack the individ-
ual uniqueness that for instance DNA evidence rest on.
As a result, estimated crime links are associated with
erroneous links, both false positives (erroneous links)
and false negatives (missed links). As with statistical type
I and II errors they are related to each other so that if one
is decreased the other one is increased, i.e. finding more
missed links results in more erroneous links. Methods are
needed to reduce the number of erroneous links added
when missed links are being pursued.
In this paper we investigate the use of spatio-temporal
crime data for filtering erroneous estimated crime links
by utilizing route information from the following four
online web-based direction services, Google maps, Bing
maps, Here maps and Mapquest. By comparing route du-
rations to the temporal constraints from crime reports it

is investigated if erroneous crime links, with improbable
routes between crime pairs, can be filtered out.
The outline of this paper is as follows, next related
work is covered in Section II followed by a description of
the prototype implementation in Section III. Then the ex-
periment and data used are being described in Section IV
followed by the results in Section V and discussion in
Section VI. Finally, the contributions and future work
are stated in Section VII and VIII respectively4.
II. RE LATE D WO RK
Tonkin et al. performed binary logistic regression, on
a sample containing both solved and unsolved crimes,
for distinguishing the linked crimes from unlinked [20].
The distinguishing of crimes was done across crime
categories, crime types and within crime types using ge-
ographical and temporal proximity. In order to examine
the discrimination accuracy, receiver operating character-
istic (ROC) analysis was performed on the sample. The
results from the ROC analysis showed notable levels of
discrimination accuracy across crime categories, across
crime types and within crime types. The work concludes
that behavioral crime linkage as useful in linking crimes
and assists in finding serial offenders based on behavior
of suspects among various crime scenes.
Fox and Farrington analyzed the behavioral con-
sistency in burglary styles among a sample of 405
solved burglaries that were committed on the east coast
of Florida between 2008 and 2009 [7]. The Jaccards
coefficient, forward specialization coefficient and the
Diversity index were used to determine the variation
in behavior between various serial burglars who had
committed burglaries in different offense styles. The
results from these analyses show that the serial burglars
are relatively consistent in their offense styles, allowing
for the construction of estimated series to assist the
investigation.
Iwanski et al. had developed a Criminal Move-
ment Model (CriMM) for determining the relationship
between the offenders’ activity space and awareness
space [11]. This model simulates the travel routes, that
offenders are likely to take, between offenders’ home lo-
cations and the major attractors. These simulated routes
were then compared with the actual crime locations that
are committed by the offender. In order to perform this
analysis, five major attractor locations within the Greater
Vancouver Regional District in Canada were selected.
Additionally, five years’ worth of real police data was
collected and analyzed for getting information about
offenders. The analysis showed that most of the offenders
were likely to commit crimes within their awareness
space.
Daele and Bernasco explored the existing literature
on directional consistency and proposed an enhanced
measure of directional consistency and empirically used
this measure to explore consistency in the offenders’
direction among a sample of 268 burglars (offenders) in
the Greater Hague area between 2001 and 2006 [6]. The
new measure investigated two main groups of offenders,
the first having strong directional bias and the other
had no directional consistency. The authors suggested
that directional consistency among offending patterns
are constructed by daily routines and habitual behavior.
It thus resulted in deducing that routes towards the
places visited by offender are more prone to burglaries.
The study presents that offender behavior is stable and
displays spatial consistency in their journey to crime.
Lisa et al. presented a method of risk distribution of
crime incidents that follow a linear pattern named as
hot routes [19]. This method addressed a number of the
weaknesses like unclear range settings, poor geocoding
and over smoothing associated with conventional hotspot
mapping techniques such as thematic mapping. The
method uses a linear distance to partition sections of
roads into grids. Rather than providing the visualization
of data the authors method provided a localized low level
view that makes it stand out for small-scale analysis.
However, the method also had some disadvantages of
being usable only to small sections of roads rather than
for a city-wide level. The work was done by using the
data of local bus routes in London. The method helped
in viewing sections of road that are highly prone to bus
crimes. By using the method, the analysts can compare
levels of crime and exclude the section of route that
are attached with the physical and socio-demographic
characteristics of the surrounding area.
III. IMPLEMENTATION
Over the last decade there has been a huge advance-
ment in the online direction services (ODS), such as
Google maps and Bing maps. People can utilize these
services for finding directions to various destinations, ac-
cess satellite and topographical images, as well as angled
aerial photography [12]. Most of the map services have
their own Application Programming Interfaces (API)
that are made publicly available. These APIs can be
used to integrate these online map services into different
websites in order to map coordinates to web-based maps
or to create location-aware services. In this study we
investigate the four largest freely availableODSs: Google

maps, Bing maps, Here maps and Mapquest. However,
the actual route calculations used for filtering erroneous
crimes is handled by Google maps, since that service
allowed the highest number of route requests per day
and it is also the quickest of the four candidates.
A. Google maps
Google maps was launched in 2005 and since then it
has become one of the major players in the area [8][22].
Google maps is a web based mapping service that
provides directions between different locations, through
various modes of transportation. These maps also show
additional data like traffic information, public transit,
street and road names, famous landmarks and buildings.
The available map imagery is updated daily and the
satellite imagery is no older than three years [8]. Users
can utilize the services of Google maps through their
publicly available API. Google maps API is free to use
up to 2,500 map loads per 24 hours [8]. After the free
limit is passed, it costs approximately half a US dollar
per 1,000 map loads.
B. Software interface
REST is a lightweight web service which is based on
a client-server model and it is used for retrieving and
updating data over the internet [15]. Data transactions
over the internet are carried out through the Hypertext
Transfer Protocol (HTTP) protocol, and REST uses
HTTP methods, like GET, POST, PUT and DELETE,
for data transactions. These REST services are used in
this study for retrieving the distance and travel times of
routes between different crime locations using the four
ODSs. The request to different ODS are made through
their respective Uniform Resource Identifiers (URIs).
The response from the ODS is the JavaScript Object
Notation (JSON) data.
C. ODS filtering method
After analyzing the residential burglary crime series
that were collected from the Swedish police, a filtering
method was designed that utilizes the distances and travel
duration between the crime locations using the ODSs.
This filtering is done in two phases. First phase is based
on the distances and second phase is based on the travel
duration.
1) Phase one: First, each crime series is handled
individually in sequence. For each series the included
crimes are extracted from the data and the crimes are
ordered chronologically based on the dates and times on
which the crimes occurred as shown in Table I.
TABLE I
ASA MPL E DATA OF SE RIE S OF C RIM ES .
Crimes Date Start Time Start Date End Time End
Crime 1 2016-01-01 09:00 2016-01-01 10:00
Crime 2 2016-01-02 12:30 2016-01-03 12:30
Crime 3 2016-01-02 12:30 2016-01-03 18:30
From Table I, it is difficult to tell whether the suspect
had committed crime 2or crime 3after committing crime
1due to the overlap in time. As mentioned previously,
serial crimes tend to have low spatial proximity. So,
if the distance between crime 1and crime 2is less
than distance between crime 1and crime 3then the
order 1,2,3is considered. Otherwise the order 1,3,2
is considered. It could also be possible to gain further
insights in the ordering of the crimes by using additional
parameters about the crimes, e.g. whether they occurred
in the city center or on the country side.
2) Phase two: After ordering the crimes according
to the chronological and spatial aspects in phase one,
the crimes are then filtered by removing crimes with
a travel duration that exceeds the amount of available
time for traveling between two crimes. To exemplify,
if the order of the the crimes in Table I is 1,2,3,
then first crime 1is assumed as origin and crime 2as
destination. The latitude and longitude values of these
two crimes are sent to the ODS and the travel duration
is extracted from the response. If this travel duration is
longer than the time difference between the crime 1and
2(same as t1 in Figure 1), then crime 1and crime 2
can not be part of a series and crime 2is suggested
to be removed. An additional parameter, the estimated
burglary event duration, represented as Tin Figure 1, is
also considered in this filtering method. The estimated
duration of burglary events is further discussed in the
Section V.
Next, this analysis continues until the crime-pairs in
the sequence of a series have been checked. Then the
next series is analyzed, and so on until no more series
remain.
D. Euclidean straight-line method
A trivial method using Euclidean straight-line dis-
tances between points was also used to represent state-
of-the-art. This method simply calculated the distance
in meters between two pairs of latitude and longitude
coordinates representing two crime locations. All such
calculations were made in the database holding the

Crime 1 Crime 2 Crime 3
t1 t2
TimeT
Fig. 1. Time difference t1 and t2 between crime 1 and 2, and between
crime 2 and 3 respectively. Together with the duration of the actual
burglary event Tfor crime 2.
crime data, by the use of a SQL statement. In order to
determine which speed to use, a sequential search was
done using the data set of known linked crime series.
The initial speed was 50 km/h and this value was then
increased by 10 km/h until crime began to be filtered
from the known linked series. Then, the speed variable
was decreased by 1km/h until no crimes were filtered.
The resulting speed was 70 km/h was then used in the
analysis of the crimes using the straight-line method.
IV. EXPERIM EN T SE TU P
The present study makes use of official crime data
from the Swedish police, where 1,493 crimes were
distributed over 457 known series that were linked by
a shared offender using physical evidence. In addition,
136,679 crimes were divided over 895 estimated series
linked by behavioral MO patterns rather than physical
evidence. For each of the crimes in these estimated
series a parameter-rich description of the crimes exists,
according to the coding-scheme described in [2]. There-
fore, each of these crimes have a two-page structured
checkbox-based form with approximately 120 param-
eters describing the residence, entry method, search
strategy, plaintiff’s precautions etc., filled in by law
enforcement officers at the crime scenes. Using these
collected parameters describing the crime scene a logistic
regression model was used to construct estimated series,
according to the description in [3].
A quasi experimental design was found to be best
suited for this study as there is no randomization while
selecting the sample. Convenience sampling technique
was used when the known series were selected as the
data consists of the official Swedish crime records of
2012-2013 [5]. The independent variables in this study
are spatial and temporal features of crimes, while the
dependent variable is linking residential burglaries using
travel route estimation.
A. Validation threats
One threat to the internal validity is due to inconsis-
tencies in the data concerning the spatial and temporal
parameters of the crimes. To address this threat, we
manually inspected the crime data removing cases that
included incorrect temporal and spatial parameters.
Another threat is the potential bias in which crimes the
police manages to link into series. Since we use these
series in order to validate the route calculation method,
it is possible that the validation is lacking. However, we
are positive it is better to validate the route calculation
method against the existing ground truth, than not doing
that at all.
Experimental evaluations usually affect the external
validity negatively since it is executed in a controlled
environment rather than in real world. In this study we
evaluate the link possibility between two cases by cal-
culating route directions using online direction services
based on the spatial and temporal data from official
Swedish crime records. As we rely on popular and well-
tested online direction services together with official
crime data we believe that the results are generalizable.
However, it is important to keep in mind that the study
was performed in a Swedish context.
V. RESULTS
In this section the results from the validation of the
filtering method as well as from filtering crimes from
both the known and estimated series are presented.
A. Validation using known series
First, the filtering method was applied to all crimes
in the known series dataset in order to validate it on
these links that are assumed to be correct. As such, it
should be possible to travel between each of the crimes
within any of these known series, i.e. none of the crimes
should be filtered by the filtering method. In order to
test this all routes and travel times between the crimes
within each series were calculated using each of the
four online direction services. Table II shows the average
pair-wise differences between ODSs, in both travel time
and route distance over all crimes in the known series
dataset. Google maps vs. Bing maps have the largest
discrepancy in travel time (just under five minutes) while
Here maps vs. Bing maps have the largest difference
in terms of route distance (on average 2.4km). Best
consistency in travel time is between Here maps and
Mapquest with a difference on 78 seconds, while the
smallest route difference is 308 meters between Google
maps and Mapquest. Overall, the four online direction
services show fairly consistent results.
Regarding the validation of the filtering method none
of the routes suggested by the ODSs indicated any

Fig. 2. The number of crimes per estimated series before and after filtering crime links using route calculations.
TABLE II
DIFF ERE NC E BET WE EN TH E DI FFER EN T ONL IN E DIREC TION
SE RVIC ES IN TER MS OF BOTH T RAVE L TIM E (IN SECONDS)IN TOP
HA LF OF T HE TAB LE ,AND DISTANCE (IN METERS)IN BOTTO M
HA LF OF T HE TAB LE .
Google Bing maps Here maps Mapquest
Google maps — 254s 126s 97s
Bing maps 1125m — 80s 236s
Here maps 427m 2381m — 78s
Mapquest 308m 1347m 558m —
erroneous crime links between any crimes in the known
series dataset. In other words, it was possible to travel
between the crimes in each of the known series using
the routes of the ODSs without breaking any temporal
constraints in the crime records.
B. Filtering estimated series using route calculation
Since the filtering method passed the validation it was
investigated to what extent erroneous crime links could
be identified in the estimated series. An erroneous crime
link in this case means that it isn’t possible to travel
between two crimes using the routes from the ODSs
without breaking the temporal constraints enforced by
the date and time entries associated with each crime in
the crime reports.
So, the travel route and duration per crime-pair in each
estimated series were calculated using Google maps. As
these routes were summarized and compared with the
temporal constraints of the crimes it turned out that
6,063 (4.4%) crimes were suggested to be removed
since it wasn’t possible to travel between them in the
time available. Table III shows the difference in number
of crimes in the estimated series dataset both before and
after filtering erroneous links. As can be seen both the
median and mean number of crimes per series decreases
after the filtering method was applied. Additionally,
Figure 2 shows how the number of removed crimes were
distributed between the 895 estimated crime series. The
number of crimes removed were fairly evenly divided
between the 895 series, with an average of 6.7crimes
being removed from each estimated series.
TABLE III
NUM BER O F CR IME S IN T HE ES TI MATE D CRI ME S ERI ES B OTH
BE FOR E AN D AFT ER FI LTER ING U SI NG RO UTE C AL CUL ATIO NS .
Min Median Mean Std.dev. Max
Before filtering 2 155 153 68 358
After filtering 2 146 145 66 352
Cohen’s d was used to measure the overlap between
the number of crimes in estimated series before and
after filtering was applied. Cohen’s d is usually used in
statistical analysis for estimating the difference between
two distributions [4]. It is calculated by dividing the
difference between the means with the pooled SD of the
two distributions. The difference in number of crimes per
estimated crime series before compared to after filtering

is 0.12, i.e. a small difference. Also, this means that the
overlap of the two distributions is 92.3%.
C. Filtering estimated series using Euclidean distances
The filtering method using Euclidean distances was
applied to the crimes in the estimated crime series. The
result show that a total of 3,394 (2.5%) erroneous
crime links were removed from the estimated series. It
is clear that the route-based filtering method performed
better since it managed to remove 6,063 crime links.
So, compared to filtering using Euclidean distances the
route-based filtering managed to remove 79 % more
erroneous crime links.
D. Estimating the duration of burglary events
Finally, in an attempt to estimate the amount of time
available for a burglar to carry out a burglary event, an
analysis of the time difference between the arrival time
at the crime scene and the latest departure time required
in order to make it to the next crime in the series was
carried out. It should be noted that this analysis only is
possible for crimes that are not the first or the last crime
in series, i.e. the crime to investigate must be surrounded
by at least one crime before and after in time. Given these
requirements, the analysis is identical to estimating Tin
Figure 1.
In order to find the time that a burglar takes to commit
a burglary, the proposed filtering method was applied to
the known series dataset. However, only crime series
containing at least three crimes were included, there
were 216 such crime series (1,011 crimes), since only
crimes in the middle of series can be analyzed. Then
the parameter Tfrom Figure 1 was introduced in the
proposed filtering method. When a burglar commits a
particular residential burglary, then it is implied that the
burglar spends time at that respective residence. Usually
this time varies from crime to crime due to various
factors like entry method and type of stolen goods.
Considering the example in Figure 1 then t1 and t2 can
be obtained from the four ODSs included in the study.
Next, the value of Tis incremented from zero until the
burglar must leave the crime scene in order to make it
to the next crime in the series. After running a series
of tests on each of the 216 known series, the results in
Table IV were summarized.
The results in Table IV indicate that the burglary
events could have a duration up to approximately 20
minutes (1,200 seconds). The mean duration over all
four ODS is 907 seconds or about 15 minutes, i.e. on
average these burglars spent up to 15 minutes on the
TABLE IV
THE S UMM ARY O F BUR GL ARY DU RATI ON (IN SECONDS)
CALCULATED USING FOUR DIFFERENT ONLINE DIRECTION
SE RVIC ES.
Min Median Mean Std. dev. Max
Google maps 300 1065 899 342 1200
Bing maps 333 1078 911 343 1260
Here maps 360 1082 915 339 1260
Mapquest 300 1072 901 343 1200
crime scene and still had sufficient time to travel to the
next crime location. However, do note that these results
only are a first indication based on a potentially biased
subset of the dataset.
VI. DISCUSSION
The results presented in the previous section indicate
that ODSs can be used for filtering erroneous crime
links from estimated series. Further it is also clear that
filtering based on actual route calculations perform better
than Euclidean straight-line methods. However, filtering
crime links using travel routes comes with a number of
drawbacks. First, it involves more complex computation
compared to methods that rely on traditional Euclidean
distances, and as such the former methods take more
time to compute. Table V presents the total time required
for each of the four ODSs for calculating the routes for
1493 crimes in each of the 457 known series. As can be
seen Google maps has the shortest time with about two
minutes compared to Mapquest that requires almost nine
minutes for the same job, roughly 4.4times more time.
TABLE V
TOTAL T IME R EQUIR ED FOR FILTERI NG A LL KN OWN S ER IES F OR
EAC H ODS.
Total time (in seconds)
Google maps 121
Bing maps 283
Here maps 197
Mapquest 522
Another drawback is that the filtering efficiency will
differ depending on which means of travel is analyzed,
e.g. walking, driving etc., and in this initial study we
have only relied on driving as the mode of transportation.
However, further research could investigate how a com-
bination of different transportation modes would affect
the end result. Potentially using heuristic to choose the
most appropriate means of travel for each crime pair.

Additionally, it would be interesting to investigate the
effect of applying scaling factors to the route duration
in order to address offenders not obeying speed limits.
As an example, a route between two crime sites was
estimated to take 20 minutes, but the burglar did not
obey the speed limits and drove the same distance in 15
minutes. The effect could be that the crime link between
these two crimes were removed because there wasn’t
room for 20 minutes’ travel time, while on the other
hand 15 minutes would just make it.
Yet another drawback has to do with data confiden-
tiality and privacy, as law enforcement agencies must
share the crime coordinates with the online direction
service provider in order to use their routing services.
It is important that law enforcement agencies are aware
of this and develop policies that address potential threats
to data confidentiality and privacy.
Despite the drawbacks listed above, we believe that
using ODSs for identifying and filtering erroneous crime
links is an approach worth pursuing further. If online
direction services are being used it is both time and cost
effective. Although it comes with a number of drawbacks
it should be clear that so does traditional methods based
on Euclidean distances. Finally, filtering little over 4%
of the crimes in estimated series could seem a marginal
effect. However, this is a cost-efficient and rather simple
method that can reduce erroneous crime from series.
Together with additional filtering methods the total effect
of removed crimes could add up. Allowing erroneous
crimes to be removed from estimated crime series before
any human investigatory resources are being invested.
VII. CONCLUSION
In this study we investigate a method that relies on
freely available online direction services, such as Google
maps, for identifying and filtering erroneous crime links
in 895 estimated crime series linked by soft evidence,
e.g. offender behaviors. A prototype was implemented
and validated on a set of 457 known crime series linked
by physical evidence such as DNA. In the validation
it was found that all known series passed the filtering
method. When the same method was applied on the
estimated series 6,063 (4.4%) were filtered out. The pro-
posed filtering method was also compared to a traditional
method relying on Euclidean straight-line distances. In
this comparison the proposed method managed to filter
79 % more erroneous crime links compared to the
state-of-the-art method. Finally, a chronological analysis
of crime series including route analysis indicates that
burglars on average have up to 15 minutes to spend on
the actual burglary event.
VIII. FUT UR E WORK
Future work could investigate the impact of different
travel modes, e.g. walking or driving, on the filtering
capability of erroneous crime links. It would also be
interesting to analyze the impact of applying scaling
factors to the route duration in order to address situations
where offenders do not obey the speed limits which
online direction services are based on.
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