A Novel Clustering Algorithm to Capture Utility Information in
Transactional Data
Piyush Lakhawat, Mayank Mishra and Arun Somani
Department of Electrical and Computer Engineering, Iowa State University, Ames, Iowa, U.S.A.
Keywords:
Clustering Algorithm, Transactional Data, High Utility Patterns.
Abstract:
We develop and design a novel clustering algorithm to capture utility information in transactional data. Trans-
actional data is a special type of categorical data where transactions can be of varying length. A key objective
for all categorical data analysis is pattern recognition. Therefore, transactional clustering algorithms focus
on capturing the information on high frequency patterns from the data in the clusters. In recent times, utility
information for category types in the data has been added to the transactional data model for a more realistic
representation of data. As a result, the key information of interest has become high utility patterns instead of
high frequency patterns. To the best our knowledge, no existing clustering algorithm for transactional data
captures the utility information in the clusters found. Along with our new clustering rationale we also de-
velop corresponding metrics for evaluating quality of clusters found. Experiments on real datasets show that
the clusters found by our algorithm successfully capture the high utility patterns in the data. Comparative
experiments with other clustering algorithms further illustrate the effectiveness of our algorithm.
1 INTRODUCTION AND
MOTIVATION
Transactional data model is used in many important
applications of data mining and analytics like market
basket analysis, bioinformatics, click stream analysis
etc. Clustering is one of key analysis techniques for
these applications. For example, clustering of cus-
tomer transactions data is performed in market basket
analysis for segmentation and identification of vari-
ous customer types (Ngai et al., 2009). An impor-
tant data type in bioinformatics experiments is gene
co-expression data which can be modeled as transac-
tional data (Andreopoulos et al., 2009). Identifying
clusters of genes exhibiting similar expression in con-
trolled conditions can lead to critical discoveries in
medicine.
A typical transaction of size k in a transactional
data set can represented as T
ID
=(X
1
, X
2
. . . X
K
), where
X
i
is a category type(also called item type) and ID
is the transaction ID. For example, transactions from
a retail store data can be like T
1
=(Candy, Pop,
Chips), T
2
=(HDTV, Hi-Definition Speakers) and so
on, where each transaction is a list of items bought
by a customer in one trip to the store. If we work
with only this level of information then we assume
equal importance of each category type in the analy-
sis. This would mean that if more number of customer
purchase patterns include Pop than HDTVs then our
analysis would implicitly assume Pop being a more
important category type. However, due to signifi-
cantly more profit per sale of a HDTV, it is possible
that overall HDTV sales yield much more profit to the
store than Pop sales. The general idea is that various
category types in a transactional data have different
level of relative importance (called utility) in the anal-
ysis. Therefore to make the transactional data model
more realistic utility values are assigned to each cate-
gory type in the data. An important data mining prob-
lem which also uses transactional data model is item-
set mining. The aforementioned idea has led to the
evolution of traditional frequent itemset mining prob-
lem into the current high utility itemset mining prob-
lem (Tseng et al., 2015). Such a transition has not yet
occurred for the transactional data clustering problem.
To the best of our knowledge no existing clustering al-
gorithm for transactional data captures the utility in-
formation.
Current transactional clustering algorithms cap-
ture the frequency information (number of occur-
rences) while finding clusters (Yan et al., 2010) but do
not use the utility values. This will lead to misleading
clusters especially when various category types have
significant difference in their utility. In order to cap-
456
Lakhawat, P., Mishra, M. and Somani, A.
A Novel Clustering Algorithm to Capture Utility Information in Transactional Data.
DOI: 10.5220/0006092104560462
In Proceedings of the 8th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2016) - Volume 1: KDIR, pages 456-462
ISBN: 978-989-758-203-5
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

ture high utility patterns (patterns based on combina-
tion of frequency and utility) in the data, we propose a
concept of relative utility of category types in clusters.
We use it to define a new similarity metric to guide
the clustering process. Based on our similarity met-
ric we develop a hierarchical agglomerative clustering
algorithm. The algorithm design allows two tunable
parameters to be set to achieve clusters with desired
properties. Since we are introducing a new clustering
rationale, we propose two corresponding cluster eval-
uation criterion as the existing ones dont take utility
values into account.
1.1 Contributions
Our work makes the following contributions:
• A novel clustering algorithm to capture utility in-
formation in transactional data. The algorithm can
be tuned to obtain clusters with desired properties
of a strong core and a balanced structure.
• Two validation criterion for evaluating the ob-
tained cluster structure based on how accurately
it captures the high utility patterns in the data.
• Experimental results on real data sets showing
that the clustering algorithm successfully captures
the high utility patterns in the data. Compara-
tive experiments with other algorithms illustrate
the effectiveness of our algorithm.
2 PRIOR WORK ON
CATEGORICAL AND
TRANSACTIONAL
CLUSTERING
Transactional data is a special type of categorical data
where transactions can be of varying lengths. While it
is possible to use categorical clustering algorithms for
transactional data, most of them lead to a data explo-
sion problem as described in (Yan et al., 2010). Spe-
cific algorithms targeting transactional data cluster-
ing have been developed as well (Wang et al., 1999),
(Yan et al., 2005), (Yan et al., 2010), (Yang et al.,
2002). Use of similarity measures and cluster quality
measures are two common approaches used in most
of the categorical and transactional clustering algo-
rithms. Based on our review of the published work
we classify them into the following three categories:
• Similarity Measures. In (Huang, 1998) an ex-
tension of the popular k-means algorithm (which
is for numerical data) is presented called k modes.
It replaces the means with modes of clusters to
minimize a cost function. An in-depth analysis
of subsequent updates of the k-modes algorithm
is done in (Bai et al., 2013). In (Guha et al.,
1999) a link based similarity measure is proposed
to guide the clustering. An entropy based similar-
ity criterion is presented in (Chen and Liu, 2005).
A transformation technique is presented in (Qian
et al., 2015) to map categorical data into a space
structure followed by using similarity measures.
A similarity measure based using information bot-
tleneck theory is presented in (Tishby and Slonim,
2000) and (Andritsos et al., 2004). (Ganti et al.,
1999), (Gibson et al., 1998) and (Wang et al.,
1999) are some other works with the focus on sim-
ilarity type measures for clustering. A mapping of
categorical data into a tree structure is performed
in (Chen et al., 2016) before performing cluster-
ing using a tree similarity metric.
• Quality Measures. (Yang et al., 2002), (Yan
et al., 2005), (Barbar
´
a et al., 2002) and (Yan
et al., 2010) present algorithms which iteratively
improve overall cluster quality. These definitions
are based on various entropy based concepts from
information theory. An in-depth discussion of en-
tropy based criterion used for the categorical clus-
tering is presented in (Li et al., 2004).
• Miscellaneous. Categorical clustering has been
presented as an optimization problem in (Xiong
et al., 2012). A learning based multi-objective
fuzzy approach is presented in (Saha and Maulik,
2014). An entropy based subspace clustering
technique for categorical data is presented in (Sun
et al., 2015).
While the current body of work has numerous clus-
tering algorithms, all lack of capturing the utility in-
formation in the data. We propose the following algo-
rithm to fill the void.
3 A NOVEL CLUSTERING
ALGORITHM TO CAPTURE
UTILITY INFORMATION IN
TRANSACTIONAL DATA
Any clustering algorithm is designed with a clustering
criterion at its core. The clustering criterion behind
our algorithm is to gather transactions which share
common high utility category types in a cluster. At the
convergence of clustering we expect to capture high
utility patterns of the data. While the current algo-
rithms for transactional clustering aim to capture high
frequency patterns while clustering, we argue that this
A Novel Clustering Algorithm to Capture Utility Information in Transactional Data
457

can lead to inaccurate clustering in cases where the
utilities of category types have a steep distribution. A
high utility cluster (containing transactions with com-
mon high utility category types) can be missed (i.e.
not found) if we focus only on frequency information
while clustering. Before further describing our clus-
tering algorithm in detail we need to define the fol-
lowing preliminaries (common in utility itemset min-
ing (Tseng et al., 2015)):
I = {a
1
, a
2
, . . . , a
M
} = Set of item(category) types
(1)
D = {T
1
, T
2
, . . . , T
N
} = Transactional dataset (2)
where each T
i
= {x
1
, x
2
, . . .} ⊂ I
X = size k itemset = {x
1
, x
2
, . . . , x
k
|x
i
∈ I} (3)
eu(a
i
) = external utility of a
i
(4)
iu(a
i
, T
j
) = internal utility of a
i
in T
j
(5)
eu(a
i
) is the measure of unit importance for item type
a
i
. While iu(a
i
, T
j
) is a quantity measure of a
i
in T
j
.
The absolute utility of an item in a transaction is de-
fined as the product of its internal and external utility.
au(a
i
, T
j
) = eu(a
i
).iu(a
i
, T
j
) (6)
Absolute utility of an itemset in a transaction is the
sum of absolute utilities of its constituent items.
au(X, T
j
) =
∑
x
i
∈X
au(x
i
, T
j
) (7)
Absolute utility of a transaction (also called transac-
tion utility) is the sum of absolute utilities of all its
constituent items.
TU(T
j
) =
∑
x
i
∈T
j
au(x
i
, T
j
) (8)
Absolute utility of an itemset in the dataset D is the
sum of absolute of that itemset in all transactions that
it occurs in.
au(X, D) =
∑
X∈T
j
∧T
j
∈D
au(X, T
j
) (9)
The set of HUI in D is the collection of all itemsets
which have absolute utility more than or equal to φ in
the dataset D.
HUI in D = {X such that au(X, D) ≥ φ} (10)
A cluster C
k
of is a subset of transactions from D.
C
k
= {T
1
, T
2
. . . T
k
|T
i
∈ D} (11)
C is the set of all given clusters.
I
C
k
= {a
i
|a
i
∈ T
j
∧ T
j
∈ C
k
} = item types in C
k
(12)
We introduce following new concepts of cluster
utility, relative utility of a category type in a cluster
and the affinity between clusters.
CU(C
k
) =
∑
T
j
∈C
k
TU(T
j
) = Cluster utility of C
k
(13)
We define cluster utility as an overall measure of im-
portance of a cluster, since it is the sum of utilities of
all transactions in it.
∀a
i
∈ I
C
k
, ru(a
i
,C
k
) =
∑
a
i
∈I
C
k
∧T
j
∈C
k
au(a
i
, T
j
)
CU(C
k
)
(14)
= relative utility of a
i
in C
k
We define relative utility as the relative impor-
tance (since utility is a unit of importance) given to
a
i
among all I
C
k
in C
k
. The set {ru(a
i
,C
k
)|a
i
∈ I
C
k
} is
then a of signature of the cluster. It is a concise rep-
resentation of the utility information we are interested
in about the cluster. And the collection of all such sets
gives us the concise global information of the cluster
structure present in the dataset on the basis of high
utility patterns in it.
For clusters C
i
and C
j
:
a f f inity(C
i
,C
j
) =
∑
a∈I
C
k
∧a∈I
C
j
min(ru(a,C
i
), ru(a,C
j
))
(15)
We define affinity as the sum of shared utility of
common category types among two clusters. So it is a
representative of the similar importance given by two
clusters to their common category types. This aligns
with our goal of clustering which is to gather transac-
tions which share common high utility category types
in a cluster.
3.1 Clustering Algorithm
Using our definition of affinity we perform clustering
on the dataset using a bottom-up (also called agglom-
erative) hierarchical approach. Agglomerative hier-
archical approach is well established for successful
clustering of categorical data(Guha et al., 1999). We
initialize our algorithm by assigning each transaction
as an individual cluster. We then calculate affinity of
each cluster with every other cluster. Following that
we incrementally merge the two clusters which have
most affinity to each other. A merge implies union of
the two clusters to form a single cluster. After each
merge we calculate all the affinity values associated
with the new cluster. This includes first computing the
cluster utility and relative utilities for the new cluster.
The cluster structure represents a complete graph
with each cluster as a node connected to every other
node. The node weights represent the cluster utility
and the edge weights represent the affinity values. At
KDIR 2016 - 8th International Conference on Knowledge Discovery and Information Retrieval
458

each merge we calculate the node weight for the new
node and the edge weights for the new edges while
keeping the graph complete. We terminate the al-
gorithm when the maximum affinity found between
any two clusters is below a certain predefined affinity
threshold min
a f f
. The cluster distribution can have
a long tail, meaning there can be many transactions
which do not fall under any significant cluster struc-
ture. min
a f f
ensures that clusters with high cluster
utility do not end up merging just because all other re-
maining small clusters are very dissimilar among each
other.
At this point we only select clusters with more
than or equal to a minimum cluster utility value. We
do this by predefining a parameter min
uty
and accept-
ing only those clusters which have cluster utility more
than or equal to min
uty
th
of the cluster with the max-
imum cluster utility. Figure 1 shows a small syn-
thetic example illustrating the clustering process. It
shows affinities and cluster utilities as edge and node
weights respectively. The change in cluster structure
can be observed based on the choice of min
a f f
and
the min
uty
parameters. Algorithm 1 below provides a
pseudocode.
Input: C ;
while max
a f f
≥ min
a f f
do
for C
i
,C
j
∈ C do
if affinity(C
i
,C
j
) > max
a f f
then
max
a f f
= affinity(C
i
,C
j
);
C
m1
= C
i
;
C
m2
= C
j
;
merge(C
m1
,C
m2
);
update relevant affinities;
for C
t
∈ C do
if
CU(C
t
)
max(CU(C
k
)∀C
k
∈C)
≤ min
uty
then
delete C
t
;
return C;
Algorithm 1: A novel clustering algorithm for categorical
data with utility information.
4 PROPERTIES OF THE
CLUSTER STRUCTURE
The obtained cluster structure by our algorithm will
have the following properties by design:
• A strong core: We terminate the clustering pro-
cess when the maximum affinity found between
any two clusters is less than min
a f f
. Therefore,
each cluster will have a set of category types for
which each transaction in the cluster has at least
Figure 1: Illustration of the clustering process.
min
a f f
of shared relative utility among them.
This is evident from the definition of affinity.
• A balanced structure: Ratio of cluster utility of
each cluster to that of the cluster with the maxi-
mum cluster utility will be more than or equal to
the predefined threshold min
uty
.
• Greedy path taken: Clusters with the most affinity
with each other merge at each step.
Besides the above three properties, we expect the
cluster structure to capture the high utility patterns in
the data. This is the primary goal of this work. A re-
cent transactional clustering framework SCALE(Yan
et al., 2010) introduces a cluster validation crite-
rion called LISR(Large Item Size Ratio) which cap-
tures large items(frequently occurring category types)
preserved in clustering. Since we capture patterns
based on combination criterion of frequency and util-
ity, using validation criterion like LISR is inadequate.
Therefore we introduce two new validation criterion
based on the high utility itemsets (HUI) present in the
clusters. We call them HUI
capture
and HUI
inaccurate
.
They are defined as follows:
HUI in C = {X such that au(X,C
k
) >= φ
0
|C
k
∈ C}
(16)
where φ
0
=
φ
|D|
∑
C
k
∈C
|C
k
|
.
The set of HUI in C represents the high utility pat-
terns present in the cluster structure C. If the entire
data set D is used in clustering then φ = φ
0
. How-
ever, since clustering is an expensive operation often
random sampling techniques are used to select trans-
actions for clustering. In those cases we scale down
the threshold φ to φ
0
.
HU I
capture
=
|{HUI in C} ∩ {HUI in D}|
|{HUI in D}|
(17)
HU I
capture
represents the degree to which the
cluster structure C captures the high utility patterns
A Novel Clustering Algorithm to Capture Utility Information in Transactional Data
459

present in the dataset D. Successful HU I
capture
is
characterized by a value greater than the ratio of size
of data used for clustering to the size of the whole
dataset
∑
C
k
∈C
|C
k
|
|D|
. Higher values of HUI
capture
imply
higher quality of the cluster structure.
HU I
inaccurate
=
|{HUI in C} − {HUI in C ∩ HUI in D}|
|{HUI in D}|
(18)
HU I
inaccurate
represents the degree of inaccurately
captured high utility patterns in C with respect to the
high utility patterns present in the data D. Lower val-
ues of HUI
inaccurate
imply higher quality of the cluster
structure.
5 EXPERIMENTAL EVALUATION
AND DISCUSSION
To validate our algorithm we perform clustering on a
real data set obtained from (Ret, 2003) and provided
by (Brijs et al., 1999). It contains anonymous cus-
tomer transaction data from a Belgian retail store and
contains 88,163 transactions. We randomly generated
the external utilities (between 1-50) for various cate-
gory types by using a uniform random number gen-
erator. Using this data we performed the following
experiment:
• For φ=50000 we calculated the list of high utility
itemsets (HUI) in the complete data set D. We
found 111 HUIs. We did this by implementing a
popular itemset mining technique called the two-
phase algorithm (Liu et al., 2005). The choice of
φ was based on obtaining a reasonably large but
manageable number of HUI.
• For four combinations of our algorithm parame-
ters we calculated the cluster structure and the list
of HUI for each cluster structures. The selection
of data for clustering is done using uniform ran-
dom sampling.
• Finally, we evaluate our validation metrics:
HU I
capture
and HU I
inaccurate
. We present the re-
sults in Figure 2.
The following inferences can be drawn from the
results:
• The HUI captured in clusters are significantly
greater than the data used for clustering. This im-
plies high quality of the cluster structure.
• The extremely low (and 0) values of HUI inaccu-
rately captured imply high accuracy of the cluster
structure.
Figure 2: Cluster validations metrics for the retail store data
set.
Table 1: Comparative results for Soybean dataset: patterns
missed.
φ
φ
φ Our Algorithm BKPlot K-modes
800 0 0 8
400 2 5 7
200 0 2 4
We also perform comparative experiments with
two other categorical clustering algorithms: K-modes
(Huang, 1998) and BKPlot (Chen and Liu, 2005).
Since the provided implementations of K-modes
(Kmo, 2015) and BKPlot (BKP, 2008) accept data
sets only with uniform transaction length, we perform
the comparative analysis on the Soybean data set ob-
tained from (UCI, 1987). It is a collection of attributes
of various soybean plants type. Soybean data set is
reasonably small so we dont use the random sampling
and instead perform clustering on the entire dataset.
To maintain uniformity in cluster structure we eval-
uate a four cluster solution for each algorithm. For
using in our algorithm we also generate utility val-
ues(between 1-50) for each category type using a uni-
form random number generator. Since the data set is
small and we dont use random sampling, we perform
comparison based on patterns (high utility itemsets)
missed by clusters formed by each algorithm. Ta-
ble 1 shows the comparative results. φ represents the
threshold value used to calculate high utility patterns
(itemsets). Our algorithm performs better (or equal)
than the other two for all cases. While the soybean
data set is a small one, it still illustrates the fact that
well established algorithms like K-modes and BKPlot
miss out on high utility patterns.
6 CONCLUSIONS AND FUTURE
WORKS
In the growing body of work of clustering algorithms
for categorical data we identified the need for an al-
gorithm which captures the utility information in the
transactional data. The current algorithms for trans-
KDIR 2016 - 8th International Conference on Knowledge Discovery and Information Retrieval
460

actional clustering aim to capture high frequency pat-
terns while clustering. We argue that this can re-
sult in misleading clusters especially for cases where
the utilities of category types have a steep distribu-
tion. High utility clusters can be missed if we focus
only on frequency information while clustering. We
propose a novel clustering algorithm for transactional
data which captures the utility information. We also
propose two validation criterion for the obtained clus-
ter structure based on how accurately it captures the
high utility patterns in the data.
Our experiments on a real data sets show that the
clustering algorithm successfully captures the high
utility patterns in the data. Our comparative experi-
ment results further illustrate the effectiveness of our
algorithm over the popular K-modes and BKPlot al-
gorithms. For future work, we plan to do experiments
on data sets from various applications like bioinfor-
matics, click stream data etc. We believe interpreta-
tions of clusters found in different data sets will lead
to interesting results and evolution of our algorithm.
We plan to develop the idea of utility aware clustering
for entropy based clustering methods as well.
ACKNOWLEDGEMENTS
The research reported in this paper is funded in part
by Philip and Virginia Sproul Professorship Endow-
ment and Jerry R. Junkins Endowments at Iowa State
University. The research computation is supported
by the HPC@ISU equipment at Iowa State Univer-
sity, some of which has been purchased through fund-
ing provided by NSF under MRI grant number CNS
1229081 and CRI grant number 1205413. Any opin-
ions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the funding
agencies.
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