Data Mining Techniques for Autonomous Exploration of
Large Volumes of Geo-referenced Crime Data
Vladimir Estivill-Castro and Ickjai Lee
Department of Computer Science & Software Engineering
The University of Newcastle
Callaghan, NSW 2308, Australia
{vlad, ijlee}@cs.newcastle.edu.au
Abstract. We incorporate two knowledge discovery techniques, clustering and association-rule mining, into a fruitful
exploratory tool for the discovery of spatio-temporal patterns. This tool is an autonomous pattern detector to reveal
plausible cause-effect associations between layers of point and area data. We present two methods for this exploratory
analysis and we detail algorithms to effectively explore geo-referenced data. We illustrate the algorithms with real crime
data. We demonstrate our approach to a new type of analysis of the spatio-temporal dimensions of records of criminal
events. We hope this will lead to new approaches in the exploration of large volumes of spatio-temporal data.
Keywords. Spatio-temporal association rules. Exploratory data analysis. Knowledge Discovery and Data Mining.

1.

INTRODUCTION

Learning cause-effect associations and exercising
control over a complex phenomenon like crime can only
be accomplished by domain knowledge and thorough
understanding. Raw data is too detailed and thus the
next step is to apply statistical analysis. Nevertheless,
despite being informed about a phenomenon, we may
still lack an understanding about causes or plausible
hypotheses to explain patterns in the phenomenon.
Identifying salient features contributing to frequency
concentration of crime is essential to prevention. While
geocomputation applications have penetrated the first
two stages, namely facilitating data collection and
statistical report generation, advanced autonomous
techniques in exploratory analysis are not widely
adopted. Knowledge comes from sophisticated and
exploratory analysis of the relations, associations and
statistics in the data. Data collection results in data-rich
environments but the bottleneck is in analysis and
hypothesis generation towards knowledge discovery.
Traditional spatial statistical analytical methods have
been dominant approaches for identifying spatial
patterns. However, these traditional approaches are
computationally expensive and confirmatory. In
addition, they necessitate prior information and domain
knowledge (Miller and Han, 2001). That is, these
methods confirm known or expected patterns, but do not
easily detect unknown or unexpected patterns residing
in large spatial databases. Thus, spatial statistical
analysis becomes inappropriate and unsuitable for datarich environments (Miller and Han, 2001; Openshaw,
1999; Openshaw and Alvanides, 1999).
Detecting clusters of crime incidents is important to
crime activity analysis (Levine, 1999). When clustering
for a particular layer (Besag and Newell, 1991; Marshall,
1991; Openshaw, 1987) in data-poor environments, it is

not impossible to consider information in other layers
that possibly impact on the target layer and thus likely
function as a population-at-risk since the combination of
background layers is limited to a small number. However,
it is a daunting task to incorporate all possible
background information in massive spatial databases. In
such data-rich environments, one alternative is to find
patterns of concentrations in the target layer and then
investigate possible causal factors (crime generators) or
associations (Estivill-Castro and Murray, 1998; Knorr et
al., 1996; Knorr et al., 1997) based on spatial clusters.
This approach minimizes human-generated bias and
constraints on data, which is important in exploratory
spatial analysis (Openshaw, 1987; Openshaw, 1999).
This paper reports on research for autonomous (that is,
little or no intervention from a criminologist) computer
diagnosis and pattern detection for generating highly
likely and plausible hypotheses using data mining
techniques: clustering and association rules. The
autonomous pattern detector reveals cause-effect
associations and aggregated groups of spatial
concentrations leading to expanding the knowledge and
understanding of crime. Our techniques incorporate
Knowledge Discovery and Spatial Data Mining (KDSDM) into the analysis of the spatio-temporal
dimensions of the computer records of criminal events.
Real crime data is used to demonstrate the potential of
this approach. The results of exploratory data analysis
by KD-SDM techniques do not reveal information about
individuals, but exhibit general patterns.
The rest of paper is organized as follows. Section 2
revisits clustering and association-rule mining. In
Section 3, we propose two association-rule mining
approaches using spatial clusters. Section 4 provides
experimental results with real crime data sets that confirm
the virtue of our approach. Section 5 draws conclusions.

2.

CLUSTERING AND ASSOCIATION RULES

Clustering and association-rule mining are two core
techniques in spatial data mining (Miller and Han, 2001)
and geographical data mining (Openshaw, 1999).
Clustering is closely related to intensity measurement
(first order effect) whilst association-rule mining is more
related to dependency measurement (second order
effect). Thus, the combination of these two techniques
will reveal the structure of complex geographical
phenomena, since the first order effect and the second
order effect formulate geographical phenomena (Bailey
and Gatrell, 1995).
Spatial clustering is a series of processes grouping a set
of georeferenced point-data, P = {p 1, p 2,…, p n} in some
study region S, into smaller homogeneous subgroups
due to contiguity (proximity in space). Several spatial
clustering approaches have been proposed (Eldershaw
and Hegland, 1997; Ester et al., 1996; Estivill-Castro and
Houle, 1999; Estivill-Castro and Lee, 2000a; EstivillCastro and Lee, 2000b; Kang et al., 1997; Karypis et al.,
1999; Ng and Han, 1994; Wang et al., 1997; Wang et al.,
1999; Zhang et al., 1996; Zhang et al., 2001) to detect
patterns of spatial concentrations in large spatial
databases. They have their strengths and weaknesses.
Detected spatial aggregations are indicative of
interesting areas (global hot spots and localized
excesses) that require further analysis to find causal
factors or possible correlations (Estivill-Castro and Lee,
2000a). Thus, clustering answers queries like “Where do
clusters occur?’’, “How many cluster reside in S?’’ and
provides further suggestions for investigation, like
“Why they are there?’’. Despite of the wealth of
clustering methods, relatively little research (EstivillCastro and Murray, 1998; Knorr et al., 1997) has been
conducted on post-clustering analysis (cluster
reasoning and correlation analysis using clusters). This
is due to difficulties with efficiency, effectiveness and
degree of autonomy in clustering methods, difficulty of
cluster shape extraction and lack of adequate correlation
measures. Recent clustering methods (Estivill-Castro
and Lee, 2000b; Karypis et al., 2000) using dynamic
thresholds overcome typical problems of traditional
clustering methods that use global thresholds
(Eldershaw and Hegland, 1997; Ester et al., 1996; EstivillCastro and Houle, 1999; Kang et al., 1997; Ng and Han,
1994; Wang et al., 1997; Wang et al., 1999; Zhang et al.,
1996). Thus, they are able to identify quality clusters
including clusters in heterogeneous densities and
clusters in different sizes and shapes. In addition, Lee
(Lee, 2001) proposed a robust automatic cluster shape
detection method for post-clustering analysis. It derives
cluster boundaries and approximates shapes of clusters
with the boundaries. These recent advances set the
scene for post-clustering analysis.
Association-rule mining has been a powerful tool for
discovering correlations among massive databases
(Agrawal et al., 1993). An association rule is an
expression in the form of X ⇒ Y (c%), where X is the

antecedent and Y is the consequent, X and Y are sets of
items in transactional databases, and X ∩ Y = φ . It is
interpreted as “c% of data that satisfy X also satisfy Y’’.
Here, a relational table summarizes a set of records. The
relational table has a number of rows corresponding to
transactions and a number of columns corresponding
items. The value of an item for a given record is “1” if the
item is in the transaction, “0” otherwise. From the
relational table, we mine association rules that correlate
the presence of a set of items with another set of items.
Each rule has an associated support and confidence.
Defined as follows
Support is an estimate for Pr[X ∩ Y],
confidence is an estimate for Pr[X ∩ Y] / Pr[X].
The support is the ratio of transactions that satisfy both
X and Y to the number of transactions in databases. The
confidence is the conditional probability of Y given X.
Since users are interested in large support and high
confidence (strong rules (Koperski and Han, 1995)), two
thresholds (minimum support and minimum confidence)
are used for pruning rules to find strong association
rules. The association-rule mining is to compute all
association rules satisfying user-specified minimum
support and minimum confidence constraints. Although
association-rule mining is popular in data mining
community (Agrawal et al., 1993; Agrawal and Srikant,
1994; Fayyad et al., 1996, Fu and Han, 1995), few
research (Estivill-Castro and Murray, 1998; Koperski and
Han, 1995) has been conducted on spatial association
rules. The rule
is_a(x, house) ∧ near_by(x, beach)

⇒

is_expensive(x) (95%).
is discovered by spatial association-rule mining
(Koperski and Han, 1995). The rule suggests that 95% of
houses attached to beaches are expensive. This
traditional association-rule mining uses predicates that
contain either spatial-spatial relationship (near_by) or
spatial-aspatial relationship (is_a and is_expensive).
Here, predicates are pre-defined before association-rule
mining and only rules that are somehow related to the
predicates are extracted. Defining predicates requires
domain knowledge and necessitates concept hierarchies
that are difficult to define. For instance, it is hard to
classify a house (US$200,000) as expensive or not. The
decision purely depends on domain knowledge or
personal decision. Thus, concept hierarchies are
domain-specific and thus applicability is limited to case
at hand. Also, this traditional association-rule mining is
specialized for extended-relational databases and SAND
architectures. Thus, this is not well-suited for layerbased multivariate association mining.

3. MINING MULTIVARIATE ASSOCIATIONS
USING CLUSTERING
Crime hot spot analysis is one of popular techniques to
understand complex crime activities (Levine, 1999). We
identify these crime hot spots with cluster analysis and
find possible cause-effect relations with association-rule
mining. In this section, we propose two approaches for
cluster association-rule mining. Figure 1: explains a
vertical-view approach and a horizontal-view approach.
In this example, we consider five geographical layers as
depicted in Figure 1:(a). If we pinpoint a location within
S, the location will have five associated attributes
corresponding to the five layers. Figure 1:(b) shows
these 5 attributes vertically (referred as an attribute cube
in this paper). Values of attributes become true (1) if the
location lies within regions (clusters) of corresponding
layers, false (0) otherwise. The vertical-view approach
tries to discover interesting associations from the whole
set of attribute cubes. For instance, an association rule
“layer(1) ∧ layer(2) ⇒ layer(4) (70%)” is derived if
70% of attribute cubes satisfying attribute values of
layer 1 and layer 2, also have the value true in layer 4.

for spatial concentrations. That is, particular
environments (crime generators) attract crimes and thus
result in concentrations. Spatial association mining is to
find possible attracters or some positive contributors to
spatial clusters. Noise points are the points that are not
affected by the attractors. Thus, they are ignored for
mining associations. For this task, we need a threshold
to differentiate clusters from noise points. The threshold
is not an absolute number, but a ratio in this paper since
each point-data layer has different number of points
within it. This will be further discussed later in this
section. Following subsections will discuss the two
proposed approaches in detail.
3.1 Vertical-view Approach
The vertical-view approach is similar to the popular
raster model in the sense that they model space with
regular cells. The algorithmic procedure of the verticalview approach is as follows:
1.

Find spatial clusters for point-data layers.

2.

Segment all the layers with a finite number of
regular cells (rectangles).

Figure 1: Multivariate associations mining.

(a)

(b)

(c)

The horizontal-view approach overlays all the layers into
a target layer, and then attempts to find associations
from the target layer using intersection (overlapping)
areas. Figure 1:(c) overlays the first, second and third
layers depicted in Figure 1:(a). The first and second
layers intersect while the third layer does not intersect
with the other two. Thus, the association between the
first layer and second layer is higher than that of the first
and third and that of the second and third.
In the two approaches, we only consider spatial clusters
of point-data as candidates for mining associations.
These aggregated spatial groups of concentrations
represent and summarize the distribution of P. We
believe that there are some reasons (possibly attracters)

3.

Construct a m × n relational table with the
binary {0,1} values.

4.

Apply association-rule mining to the table.

We first compute spatial clusters of point-data by
cluster analysis. After that, we segment S and construct
attribute cubes. With attribute cubes, we build a
relational m × n table with the binary domain {0,1},
where m denotes the number of attribute cubes and n
denotes the number of layers. In the table, mi[n j]= 1 if an
attribute cube mi satisfies event in a layer n j. Finally, we
mine associations that correlate the presence of a set of
layers with another set of layers. Since the relational
table of layer-based GIS is exactly the same as that of
transactional databases except layers replace items and
locations replace transactions, it is now straightforward
to discover associations among layers using traditional
association-rule mining. We illustrate this with an
example.
Figure 2: Vertical-view approach with 4 cells (the
number of layers = 4)

(a)

(b)

layer(1) ∧ layer(2)

⇒ layer(4) (66.7%).

With 50% support (loc(2) and loc(4) out of 4 attribute
cubes), 66.7% of locations, that are near-by railway
stations and have crime incidents, fall within urban
areas. In this approach, the granularity of cells plays a
critical role.
(c)

(d)

(e)

(f)

(g)

(h)

Figure 2: and Table 1 illustrate the vertical-view
approach with 4 geographical layers. Let us assume that
Figure 2:(a)-(d) show railway stations (point), crime
incidents (point), parks (area) and urban areas (area),
respectively. The first process is to find homogeneous
groups of spatial concentrations of point-data layers.
Two clusters of railway stations and one cluster of crime
incidents are shown in Figure 2:(e) and Figure 2:(f),
respectively. Noise points are ignored. Then, we frame S
with collectively exhaustive and mutually exclusive
cells. A 2 × 2 grid is used in this case. After that, we
compute a 4 × 4 relational table before we apply
association-rule mining. Table 1 describes the relational
table.
Table 1: 4 × 4 table.
loc(1)
loc(2)
loc(3)
loc(4)

layer(1)
1
1
1
1

layer(2)
1
1
0
1

layer(3)
0
1
1
1

layer(4)
0
1
1
1

In the table, layer(j) (0 ≤ j ≤ n) in columns denotes j-th
geographical layer, loc(i) (1 ≤ i ≤ m) in rows denotes ith cell (attribute cube) in S (numbered in Morton order,
Z). t[loc(i) , layer(j)] is 1 if (clustered) event in the j-th
layer occurs in loc(i) cell, and t[loc(i) , layer(j)] is 0
otherwise. For instance, t[loc(1) , layer(1)] = 1 because
members of clusters of railway stations lie within the
top-left cell as depicted in Figure 2:(e). We mine
multivariate associations from this relational table. One
of association rules is as follows:

Figure 3: Vertical-view approach with 16 cells.

loc(11)
loc(12)
loc(13)
loc(14)
loc(21)
loc(22)
loc(23)
loc(24)
loc(31)
loc(32)
loc(33)
loc(34)
loc(41)
loc(42)
loc(43)
loc(44)

(a)

(b)

(c)

(d)

Table 2: 16 × 4 table.
layer(1) layer(2) layer(3)
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0

layer(4)
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1

Figure 3: and Table 2 illustrate the vertical-view
approach with a 4 × 4 grid for the same dataset shown
in Figure 2:. Now, the bottom-right cell (attribute cube
loc(44)) in Figure 3: has values (1, 1, 0, 1) since the cell
contains (clustered) events of layers layer(1), layer(2),
and layer(4), but layer(3). With 50% support constraint,
now we are not able to find the rule “layer(1) ∧ layer(2)
⇒ layer(4)”, since its support is only 18.8% (3/16).
However, the confidence is now 100%, since all the
locations loc(24), loc(42) and loc(44) satisfying layer(1)
and layer(2), also satisfy layer(4).

One of advantages of the vertical-view approach is that
it is easy to apply transactional association-rule mining
techniques (Agrawal et al., 1993; Agrawal and Srikant,
1994; Fu and Han, 1995), since the vertical-view
approach uses relational tables. However, it has a main
drawback. That is, rules discovered by the vertical-view
approach are heavily dependent on the granularity that
is difficult to determine. Similar difficulties are found
when modeling point-data using raster-like approach.
3.2 Definitions
The following definitions are made to explain the unique
process of association-rule mining using regions of
clusters. Let P be a data layer storing point data and R a
real value in [0,1].
Definition 1. Clusters with Ratio R of P [denoted
CwR(P)] are the clusters C detected by a clustering
approach (algorithm) whose normalized sizes (the
number of points in a cluster in C / the total number of
points in P) are equal to or greater than R.
Let X and Y be sets of layers (for example X1= {P1} is a
one layer expression). The expression X will typically
identify the antecedent while we use Y for the
consequent. In our approach, clusters_areas(X1) is a set
of polygonized clusters (regions of clusters) of a pointdata layer X1 (the point-data is converted to area-data).
The function clusters_areas(X) (also sometimes we will
denote this as clusters_areas(antecedent)) is the total
area of the regions that result of the intersection of
clusters_areas(Xi), for all Xi in X. That is, consider the
overlay of clusters_areas(Xi), for all Xi in X and find the
regions that correspond to points clusters_areas(Xi), for
all Xi in X. The total area of these regions is
clusters_areas(X).
Definition 2. The Clustered Support (CS) is the ratio of
the area that satisfy both the antecedent and the
consequent to the area of study region S. That is,
CS = (clusters_areas(antecedent) ∩
clusters_areas(consequent)) / area(S).
Definition 3. The Clustered Confidence (CC) for a rule X
⇒ Y is the conditional probability of areas of CwR of
the consequent given areas of CwR of the antecedent.
That is,
CC = clusters_areas(X ∪ Y) / clusters_areas(X).
Note that, clusters_areas(X ∪ Y) is the area of the
regions where points are in a cluster for all layers. Thus,
they are in the (vertical) intersection of the layers. But,
the set of layers is the union of the layers in X and the
layers in Y.
Definition 4. A Clustered Spatial Association Rule
(CSAR) is an expression in the form of
X

⇒ Y (CC%), for X ∩ Y = φ .

The interpretation is as follows: CC% of areas of
clusters of X intersect with areas of clusters of Y.
3.3 Horizontal-view Approach
Since the vertical-view approach needs a parameter to
determine the granularity, it is regarded as an argumentdependent approach. Argument-tuning to find best-fit
values is not only difficult task, but very expensive in
terms of time consumption in data-rich environments.
Thus, KD-SDM favors argument-less or argument-free
approaches in order to reduce preprocessing time and to
minimize inconsistency of results. This is obvious from
the fact that the argument-free modeling, the Voronoi
diagram and its dual the Delaunay triangulation, has
gained popularity in point-data clustering (Eldershaw
and Hegland, 1997; Estivill-Castro and Lee, 2000a;
Estivill-Castro and Lee, 2000b; Kang et al., 1997) as an
alternative to overcome drawbacks of typical argumentdependent modeling methods such as k-nearest
neighbor neighboring, d-distance neighboring and
raster-like cell-based modeling. In this subsection, we
propose another approach for mining multivariate
associations that minimizes the need for user supplied
parameters.
The algorithmic procedure of the horizontal-view
approach is as follows:
1.

Find CwR(P) for point-data layers P in X and
Y.

2.

Extract cluster boundaries of each CwR for
point-data layers in X and Y.

3.

Compute the value of the areas of CwR for
point-data layers and the areas of area-data
layers.

4.

Overlay the antecedent and the consequent.

5.

Apply association-rule mining to detect
CSARs.

The vertical-view approach approximates shapes of
clusters and then polygonizes clusters with their
boundaries. Thus, it requires an effective clustering and
a robust cluster-to-area transformation to generate
accurate association rules.
Recently, Estivill-Castro and Lee (Estivill-Castro and
Lee, 2000b) proposed a boundary-based clustering that
utilizes dynamic thresholds rather than static thresholds.
It requires the Delaunay diagram as an underlying
proximity graph and performs clustering on the proximity
graph. It removes inconsistently long Delaunay edges
for all p ∈ P and removes inter-cluster Delaunay edges
to detect various types of clusters. It detects quality
clusters including non-convex clusters (unlike
partitioning clusterings (Estivill-Castro and Houle, 1999;
Ng and Han, 1994)) and clusters with heterogeneous
densities (unlike density-based clusterings (Ester et al.,
1996; Openshaw, 1987) and grid-based clusterings

(Wang et al., 1997; Wang et al., 1999)). It requires one
control value to explore the structure of distribution of
P. Smaller values of the control value produce strongly
cohesive clusters (smaller) while larger values of the
control value provide relatively less cohesive clusters
(larger). Typically, setting the control value to 1
produces quality clustering in most cases for twodimensional point-data. Thus, we also use 1 as the
control value in this paper unless otherwise noted.

(e)

Lee (Lee, 2001) proposed an algorithm that extracts
cluster boundaries and polygonizes clusters with their
extracted boundaries. The cluster-to-area transformation
does not demand user-supplied parameters to detect
shapes of clusters, but derives boundaries of clusters
from the distribution of P. Points within clusters are not
the only contributor to the shape of clusters, but points
belonging to other clusters affect the shape of the
cluster. It is able to polygonize not only non-convex
clusters, but clusters with holes (voids). Now, what is
available is summarized area-data rather than point-data
(Lee, 2001). This area-data approximates shapes of
clusters of point-data and represents spatial
concentrations where most points are aggregated. For
these reasons discussed above, we use the boundarybased clustering (Estivill-Castro and Lee, 2000b) and the
cluster boundary extraction approach (Lee, 2001) for
mining associations with the horizontal-view approach.

(f)

(g)

Now, we illustrate definitions made in Section 3.2 and
the procedure of the horizontal-view approach with
synthetic datasets shown in Figure 4:.

(h)

(i)

Figure 4: The process of the horizontal-view approach.

(a)

(c)

(b)

(d)

Figure 4:(a) illustrates a dataset I (the number of points =
46) while Figure 4:(b) presents dataset II (the number of
points = 50) with a common study region. Both datasets
have two spatial concentrations detected by the
boundary-based clustering and those are illustrated in
Figure 4:(c) and Figure 4:(d), respectively. We now apply
the cluster boundary extraction process (Lee, 2001) and
cluster boundaries that approximate shapes of clusters
are illustrated in Figure 4:(e) and Figure 4:(f). We
polygonize clusters with boundaries and their regions of
clusters are depicted in Figure 4:(g) and Figure 4:(h),
respectively. Figure 4:(i) illustrates an overlay of regions
of clusters of dataset I and those of dataset II. Visual
inspection indicates that clusters_areas(dataset I) and
clusters_areas(dataset II) intersect. Thus, we may notice
that dataset I and dataset II are somehow correlated
although we are not able to quantitatively define the
association between dataset I and dataset II solely
based on visual inspection. Quantitative analysis is
displayed with some numerical indicators in Table 3.
Table 3: Statistics of dataset I and dataset II.

S

clusters_areas

CS(%)

CC(%)

6940.14

100.0

N/A

dataset I

992.04

14.29

N/A

dataset II

1312.21

18.91

N/A

dataset I

⇒

401.46

5.78

40.47

401.46

5.78

30.59

dataset II
dataset II

⇒

dataset I
The area of study region area(S) is 6940.14, the total
area of the regions covered by clusters of dataset I is
denoted by clusters_areas(dataset I) and its value is
992.04. For the other dataset, clusters_areas(dataset II)
is
1312.21.
The
intersection
area
of
clusters_areas(dataset I) and clusters_areas(dataset II)
is 401.46 and thus CS of dataset I and dataset II is 5.78%
(401.46/6940.14).
With 5% of CS, we are able to derive two association
rules. They are as follows:
Rule 1: dataset I

⇒ dataset II (40.47% CC),

Rule 2: dataset II

⇒ dataset I (30.59% CC).

Rule 1 indicates that around 40% (401.46/992.04) of
locations belonging to regions in clusters of dataset I
also belong to regions in clusters of dataset II. That is,
around 40% of incidents of dataset I occur where
incidents of dataset II take place. Rule 2 is similarly
interpreted, but with 30.59% clustered confidence. We
see that the vertical-view approach quantitatively
defines asymmetric associations that suggest highly
likely and plausible hypotheses.
Since the horizontal-view approach is autonomous, it is
better suited for mining massive databases than the
vertical-view approach. Thus, the horizontal-view does
not necessitate domain knowledge, but maximizes user
friendliness. We examine complex real crime data with
the horizontal-view approach in next section to confirm
the virtue of the approach.
4. PERFORMANCE EVALUATION WITH REAL
DATASETS
Similar to most urban areas, understanding of crime
activity in the south east Queensland region1 of
Australia, where the capital city of Brisbane is located, is
important for regional planners and criminologists as
well as policing agencies. Figure 5: displays the state of
Queensland in Australia and the south east of
Queensland that continues to experience significant and
sustained population growth (Murray et al., 2001;

1

We consider 217 suburbs around Brisbane as a study
region in this paper.

Stimson and Taylor, 1999). However, raw crime data2 in
this region are too complex and extremely huge, thus it
seems to be a difficult task even for domain experts to
detect valuable patterns of crime incidents.
Crime statistics provided by Queensland Police Service
have three main categories: offences against the person,
offences against property and other offences. Offences
against the person consist of subcategories: homicide,
assaults , sexual offences, robbery, extortion, kidnapping
and other offences against the person. Offences against
property are composed of breaking and entering, arson,
other property damage, motor vehicle theft, stealing,
fraud and other offences against property. Other
offences include drug offences, prostitution, liquor,
gaming offences, trespassing and vagrancy, good order
offences, traffic and related offences and miscellaneous
offences. In addition, the subcategories could have
several subsubcategories. For instance, homicide
consists of attempted murder, conspiracy to murder,
driving causing death and manslaughter.
Figure 5: Queensland in Australia and the south east
study region of Queensland with 217 suburbs.

(a)

(b)

The complex structure of crime data is not the only
concern for crime activity analysis. We must consider
feature data (parks, railway stations, schools etc.) along
with crime data to detect the relationship of crime
activity to salient features. The volume of data becomes
easily beyond the capability of human analysis if
temporal crime data are considered. Thus, sophisticated
data mining tools, that autonomously suggest highly
likely plausible hypotheses, are greatly demanding to
deal with explosive databases.
Geographic information systems and crime mapping
software have been dominant tools for exploring crime
activity (Murray and Shyy, 2000). However, these tools
are not quantitatively exploratory, but rather visually
assistant with choropleth mapping, buffering,
overlaying, intersecting and containment operations.
Although these naïve operations may provide valuable
insights into the complex raw crime data, these are not
suitable for data-rich environments.
Figure 6: depicts three main categories of crime occurred
in the year of 1997 and three feature data in study
region. Although visual displays provide general
2

We use crime data recorded by Queensland Police Service
in the year of 1997 in the study region.

patterns, too much information causes confusion. For
illustration purpose, we only display three main types of
crime and three feature data in this paper. Figure 6:(a)
depicts 9,618 incidents of offences against the person.
And, Figure 6:(b) displays 113,618 incidents of offences
against property while Figure 6:(c) shows 2,124 incidents
of other offences in the region. Feature data, reserves
(249), parks including caravan parks (462) and schools
(306), are shown from Figure 6:(d) to Figure 6:(f).

(c)

(d)

(e)

(f)

(g)

(h)

Figure 6: Three main categories of crime incidents and
three feature data in study region.

(a)

(c)

(b)

(d)

(i)

(e)

(f)

Clustering summarizes complex distributions of raw
crime data and polygonization of clusters provides
regions of concentrations as hot spots.
Figure 7:
illustrates the horizontal-view association-rule mining
with cluster regions of real data depicted in Figure 6:.
Figure 7: Illustration of association-rule mining with the
horizontal-view approach with the real crime data
illustrated in Figure 6:.

(a)

Figures from Figure 7:(a) to Figure 7:(c) display overlaps
between clusters_areas(offences against the person)
and clusters_areas(feature data). Similarly, overlaps
between clusters_areas(offences against property) and
clusters_areas(feature data) are described from Figure
7:(d) to Figure 7:(f) and overlaps between
clusters_areas(other
offences)
and
clusters_areas(feature data) are depicted from Figure
7:(g) to Figure 7:(i). Visual inspection interprets parks
and schools are more associated with crime than
reserves.
This is quantitatively described in Table 4. Clustered
confidence (CC) of a CSAR “Offences against the
person ⇒ Reserves (44.93%)” is much lower than CC
of CSARs “Offences against the person ⇒ Parks
(85.29%)” and “Offences against the person ⇒
Schools (77.5%)”. These rules imply that more than 70%
of locations, where offences against the person occur,
are around parks and schools.

b)
Table 4: CS and CC of CSARs of the real crime data.

Offences against
the person ⇒
Reserves

CS(%)

CC(%)

15.40

44.93

Reserve ⇒
Offences against
the person
Offences against
the person ⇒
Parks
Parks ⇒
Offences against
the person
Offences against
the person ⇒
Schools
Schools ⇒
Offences against
the person
Offences against
property ⇒
Reserves
Reserves ⇒
Offences against
property
Offences against
property ⇒
Parks
Parks ⇒
Offences against
property
Offences against
property ⇒
Schools
Schools ⇒
Offences against
property
Other offences
⇒ Reserves
Reserves ⇒
Other offences
Other offences
⇒ Parks
Parks ⇒ Other
offences
Other offences
⇒ Schools
Schools

⇒

Other offences
15.40

28.35

63.89

50.99

29.23

85.29

29.23

57.33

26.56

77.50

Possible CSARs will increase exponentially as the
number of layers under study (in this case, crime types
and features) grows. Thus, it is almost impossible for
analysts to find interesting associations manually. The
horizontal-view approach automatically generates strong
CSARs with user-specified CC and CS. For instance,
with 30% minimum CC and 75% minimum CS, three
strong CSARs, when the size of the antecedent and the
size of consequent are 1, are discovered. These are as
follows:
Crime rule 1: Offences against property

⇒ Parks

(36.25% CS, 82.56% CC),
26.56

59.85

Crime rule 2: Offences against property

⇒ Schools

(33.42% CS, 76.11% CC),
20.83

47.44

Crime rule 3: Schools

⇒ Offences against property

(33.42% CS, 75.31% CC).
20.83

68.99

36.25

82.56

36.25

71.10

33.42

76.11

33.42

75.31

17.81

50.47

17.81

58.97

29.90

84.74

29.90

58.64

28.35

80.36

These rules imply that most offences against property
(more than 75%) are taking place around parks and
schools. Further, with more than 75% CC, locations of
schools imply occurrences of offences against property.
Many hypothesis can now be derived for input into a
confirmatory analysis. For example, this very simple
illustration already suggests that possibly residents
living around schools shall consider additional actions
for reducing crime against their property.
5.

FINAL REMARK

For the analysis of crime data, Knowledge Discovery
and Data Mining (KD-DM) techniques have been
applied by the FBI as a part of the investigation of the
Oklahoma City bombing the Unabomber case, and many
lower-profile crimes (Berry and Linoff, 1997). KD-DM
has also been used by Treasury Department of the US to
hunt for suspicious patterns in international funds
transfer records; patterns that may indicate money
laundering or fraud (Berry and Linoff, 1997). Australian
examples are the Health Insurance Commission of
Australia using KD-DM to investigate fraud within the
Medicare system (He et al., 1998) and NRMA Insurance
Ltd (Williams, 1999). However, in the above examples the
techniques have been limited to the attribute-oriented
side of the data and KD-DM has been attempted to the
spatio-temporal dimensions.
The where and when are crucial for patterns of crime.
Recent progress towards developing GIS for crime
analysis emphasizes the relevance that geo-reference
has to understanding patterns in crime (Hirschfield et
al., 1995). In a limited exploratory approach (Openshaw,
1994), systems have been developed to geographically
visualize patterns of vehicle crime, domestic burglaries,
drug-related crime and public disorder in inner city areas.

For example, hypotheses are typically human-generated
and reinforced with the display of the most contrasting
socio-demographic characteristics of areas with high
levels of criminal activity. This type of approach may
lead to hypotheses that relate the location patterns of
crime to the negative socio-demographic characteristics
of areas associated with these patterns (Gandhi and
Grubbs, 1996). The application of GIS technology to
crime analysis by mapping and display may use
statistical methods to produce maps delineating risk
surfaces for crime data (Lee, 1995).
These are
confirmatory analyses that for example, have contributed
to the consideration of geographic distribution of
criminal behavior as a primary factor for planning
residential neighborhoods (Gandhi and Grubbs, 1996).
However, today vast collections of spatio-temporal data
are gathered without any previous hypothesis, and less
as parts of a structured experiment. Moreover, it is
impossible that trained researchers examine all possible
interesting patterns in such huge amounts of data. We
require an intelligent assistant to process the data and to
autonomously (or at least with very little guidance)
analyze data. We have presented methods and
algorithms that increase even more the capacity of GIS
to become intelligent pattern spotters beyond just as
repositories to store, manipulate and retrieve data. Note
that, this direction complements traditional statistical
analyses on geo-referenced data. The intent is to design
and deploy autonomous partners in suggesting
hypothesis in the knowledge discovery process. We
have developed algorithms that will enable this
exploratory capability in computers within the context of
spatial data and crime data.
We have developed a supporting application3. It
supports visualization of cluster boundaries and mining
association rules.
REFERENCES

Besag, J. E. and Newell, J. (1991) “The Detection of Clusters
in Rare Diseases”, Journal of the Royal Statistical Society
A, vol. 154, pp. 143-155.
Eldershaw, C. and Hegland, M. (1997) “Cluster Analysis
using Triangulation”, in Noye, B. J, Teubner, M. D. and
Gill, A. W. (eds.), Computational Techniques and
Applications: CTAC97. World Scientific: Singapore, pp.
201-208.
Ester, M., Kriegel, H. –P., Sander, J. and Xu, X. (1996) “A
Density-Based Algorithm for Discovering Clusters in
Large Spatial Databases with Noise”, Proceedings of the
2nd International Conference on Knowledge Discovery
and Data Mining, pp. 226-231.
Estivill-Castro, V. and Murray, A. T. (1998) “Discovering
Associations in Spatial Data – An Efficient Medoid based
Approach”, Proceedings of the 2nd Pacific-Asia
Conference on Knowledge Discovery and Data Mining,
pp. 110-121.
Estivill-Castro, V. and Houle, M. E. (1999) “Robust
Clustering of Large Geo-referenced Data Sets”,
Proceedings of the 3rd Pacific-Asia Conference on
Knowledge Discovery and Data Mining, pp. 327-337.
Estivill-Castro, V. and Lee, I. (2000a) “AMOEBA:
Hierarchical Clustering Based on Spatial Proximity Using
Delaunay Diagram”, Proceedings of the 9th International
Symposium on Spatial Data Handling, pp. 7a.26-7a.41.
Estivill-Castro, V. and Lee, I. (2000b) “AUTOCLUST:
Automatic Clustering via Boundary Extraction for Mining
Massive Point-Data Sets”, Proceedings of the 5th
International Conference on Geocomputation, GC049.
Estivill-Castro, V. and Lee, I. (2000c) “AUTOCLUST+:
Automatic Clustering of Point-Data Sets in the Presence
of Obstacles”, Proceedings of the International Workshop
on Temporal, Spatial and Spatio-Temporal Data Mining,
Springer Verlag Lecture Notes in Artificial Intelligence
2007, pp. 131-144.

Agrawal, R., Imielinski, T. and Swami, A. (1993) “Mining
Association Rules between Sets of Items in Large
Databases”, Proceedings of the 1993 ACM SIGMOD
Conference, pp. 207-216.

Fayyad, U. M., Piatetsky-Shapiro, G., Smyth, P. and
Uthurusamy, R. (1996) Advances in Knowledge
Discovery and Data Mining. AAAI/MIT Press.

Agrawal, R. and Srikant, R. (1994) “Fast Algorithms for
Mining Association Rules”, Proceedings of 1994
International Conference on Very Large Data Bases, pp.
487-499.

Fu, Y. and Han, J. (1995) “Meta-Rule-Guided Mining of
Association Rules in Relational Databases”, Proceedings
of the 1st Workshop on Integration Knowledge Discovery
with Deductive and Object-Oriented Databases, pp. 3945.

Bailey, T. C. and Gatrell, A. C. (1995) Interactive Spatial
Analysis. Wiley: New York.
Berry, M.J.A. and Linoff, G. (1997) Data Mining Techniques
--- for Marketing, Sales and Customer Support. Wiley:
New York.
3

The application is implemented in the C++ programming
language using LEDA (Library of Efficient Data types
and Algorithms) version 4.2. For documentation and
code see http://www.algorithmic-solutions.com/.

Gandhi, S. and Grubbs, J.W. (1996) “Crime analysis using GIS
at the City of Orlando, Florida: implications for housing
policies”, Proceedings of the URISA Annual Conference,
pp. 122-132.
He, N., Graco, W. and Yao, X. (1998) “Applications of
Genetic Algorithms and k-Nearest Neighbour Methods in
Medical Fraud Detection”, Proceedings of the 2nd AsiaPacific Conference on Simulated Evolution and Learning

SEAL-98, Springer Verlag Lecture Notes in Computer
Science 1585, pp. 74-81.
Hirschfield, A., Brown, P. and Todd, P. (1995) “GIS and the
analysis of spatially-referenced crime data: Experiences in
Merseyside, UK”, International Journal of Geographic
Information Systems, vol. 9, no. 2, pp. 191-210.
Kang, I., Kim, T. and Li, K. (1997) “A Spatial Data Mining
Method by Delaunay Triangulation”, Proceedings of the
5th International Workshop on Advances in Geographic
Information Systems, pp. 35-39.
Karypis, G., Han, E. and Kumar, V. (1999) “CHAMELEON:
A Hierarchical Clustering Algorithm Using Dynamic
Modeling”, IEEE Computer: Special Issue on Data
Analysis and Mining, vol. 32, no. 8, pp. 68-75.
Knorr, E. M., Ng, R. T. and Shilvock, D. L. (1996) “Finding
Aggregate Proximity Relationships and Commonalities in
Spatial Data M innings”, IEEE Transactions on
Knowledge and Data Engineering, vol. 8, no. 6, pp. 884897.
Knorr, E. M., Ng, R. T. and Shilvock, D. L. (1997) “Finding
Boundary Shape Matching Relationships in Spatial
Data”, Proceedings of the 5th International Symposium on
Spatial Databases, pp. 29-46.
Koperski, K. and Han, J. (1995) “Discovery of Spatial
Association Rules in Geographic Information Databases”,
Proceedings of the 4th International Symposium on Large
Spatial Databases, pp. 47-66.
Lee, I. (2001) “Polygonization of Point Clusters through
Cluster Boundary Extraction for Spatial Data Mining”,
Technical Report 2000-08, The University of Newcastle,
Australia.
Lee, J. (1995) “Point pattern analysis with density estimation
for frequency data”, GIS/LIS-95 Annual Conference and
Exposition, American Soc. Photogrammetry and Remote
Sensing, pp. 598-607.
Levine, N. (1999) “CrimeStat: A Spatial Statistics Program for
the Analysis of Crime Incident Locations”, Proceedings
of the 4th International Conference on Geocomputation.
Marshall, R. J. (1991) “A Review of Methods for the
Statistical Analysis of Spatial Patterns of Disease”,
Journal of the Royal Statistical Society, A, vol. 154, pp.
421-441.
Miller, H. J. and Han, J. (2001) Geographic Data Mining and
Knowledge Discovery: An Overview. Cambridge
University Press: Cambridge, in press.
Mehlhorn, K. and Naher, S. (1999) LEDA A platform for
combinatorial and geometric computing. Cambridge
University Press: Cambridge.
Murray, A. and Shyy, T. (2000) “Integrating Attribute and
Space Characteristics in Choropleth Display and Spatial
Data Mining”, International Journal of Geographical
Information Science, vol. 14, pp. 649-667.

Murray, A., McGuffog, I., Western, J. and Mullins, P. (2001),
“Exploratory Spatial Data Analysis Techniques for
Examining Urban Crime”, British Journal of Criminology,
vol. 41, pp. 309-329.
Ng, R. T. and Han, J. (1994) “Efficient and Effective
Clustering Method for Spatial Data Mining”, Proceedings
of the 20th International Conference on Very Large Data
Bases, pp. 144-155.
Openshaw, S. (1987) “A Mark 1: Geographical Analysis
Machine for the Automated Analysis of Point Data Sets”,
International Journal of Geographic Information Science,
vol. 1, no. 4, pp. 335-358.
Openshaw, S. (1994) “Two exploratory space-time-attribute
patterns analysers relevant to GIS”, in Fotheringham, S.
and Rogerson, P. (eds.), Spatial Analysis in GIS, Taylor
and Francis: IK, pp. 83-104.
Openshaw, S. (1999) “Geographical Data Mining: key design
issues”, Proceedings of the 4th International Conference
on Geocomputation.
Openshaw, S. and Alvanides, S. (1999) “Applying
Geocomputation to the Analysis of Spatial
Distributions”, in Longley, P. A., Goodchild, M. F.,
Maguire, D. J. and Rhind, D. W. (eds.), Geographical
Information Systems: Principles and Technical Issues,
John Wiley & Sons: New York, vol. 1, pp. 267-282.
second edition.
Stimson, R. and Taylor, S. (1999) “City profile: Brisbane”,
Cities, in press.
Wang, W., Yang, J. and Muntz, R. (1997) “STING: A
Statistical Information Grid Approach to Spatial Data
Mining”, Proceedings of the 23rd International Conference
on Very Large Data Bases, pp. 144-155.
Wang, W., Yang, J. and Muntz, R. (1999) “STING+: An
Approach to Active Spatial Data Mining”, Proceedings of
the International Conference on Data Engineering, pp.
116-125.
Williams, G. J. (1999) “Evolutionary Hot Spots Data
Mining”, Proceedings of the 3rd Pacific-Asia Conference
on Knowledge Discovery and Data Mining PAKDD-99,
Springer Verlag Lecture Notes in Artificial Intelligence
1574, pp. 184-193.
Zhang, T., Ramakrishnan, R. and Livny, M. (1996) “BIRCH:
An Efficient Data Clustering Method for Very Large
Databases”, Proceedings of the ACM SIGMOD
International Conference on Management of Data, pp.
103-114.
Zhang, B., Hsu, M. and Dayal, U. (2001) “K-Harmonic
Means – A Spatial Clustering Algorithm with Boosting”,
Proceedings of the International Workshop on Temporal
Spatial and Spatio-Temporal Data Mining, pp. 31-45.