A Soft Set-based Co-occurrence for Clustering Web User Transactions

TELKOMNIKA, Vol.15, No.3, September 2017, pp. 1344~1353
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v15i3.6382  1344
Received April 23, 2017; Revised July 9, 2017; Accepted July 25, 2017
A Soft Set-based Co-occurrence for Clustering Web
User Transactions
Edi Sutoyo*
1
, Iwan Tri Riyadi Yanto
2
, Rd Rohmat Saedudin
3
, Tutut Herawan
4
1,3
Department of Information Systems, Telkom University, Bandung, West Java, Indonesia, 40257
2
Department of Information Systems, Ahmad Dahlan University, Yogyakarta, Indonesia, 55161
4
Department of Information Systems, University of Malaya, Kuala Lumpur, Malaysia, 50603
*Corresponding author, e-mail: edisutoyo@telkomuniversity.ac.id, yanto.itr@is.uad.ac.id,
rdrohmat@telkomuniversity.ac.id, tutut@um.edu.my
Abstract
Grouping web transactions into some clusters are essential to gain a better understanding the
behavior of the users, which e-commerce companies widely use this grouping process. Therefore,
clustering web transaction is important even though it is challenging data mining issue. The problems arise
because there is uncertainty when forming clusters. Clustering web user transaction has used the rough
set theory for managing uncertainty in the clustering process. However, it suffers from high computational
complexity and low cluster purity. In this study, we propose a soft set-based co-occurrence for clustering
web user transactions. Unlike rough set approach that uses similarity approach, the novelty of this
approach uses a co-occurrence approach of soft set theory. We compare the proposed approach and
rough set approaches regarding computational complexity and cluster purity. The result demonstrates
better performance and is more effective so that lower computational complexity is achieved with the
improvement more than 100% and cluster purity is higher as compared to two previous rough set-based
approaches.
Keywords: clustering, web user transactions, web mining, rough set theory, soft set theory
Copyright © 2017 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Data mining is the procedure of extracting important information from large databanks.
It is a process of performing extraction automatically from a large data bank into knowledge or
useful information. And also, it can be regarded as an algorithmic process that takes a sample
as input and yield patterns such as classification, association rules, or clustering as an output
[1]. One of the utmost advantageous role in the process of data mining is clustering in order to
define the groups and to classify the distribution and patterns in the data. This is a process for
grouping data into multiple clusters or groups so that data in one cluster has a maximum level of
similarity and data among clusters has a minimum similarity [2]. The process that occurs is
partitioning a collection of data objects into several subsets that have homogeneous
characteristics called clusters. Objects within the cluster have similar characteristics between
each other and are different from other clusters. Partitions are not done manually but with a
clustering algorithm. Therefore, clustering is very useful and can find unknown groups or groups
in the data. There are many approaches used for data clustering, some are able to handle
uncertainty, and other improve computational complexity. Many practical and complex clustering
problems in the area of engineering, health science, environmental science, and economics are
often involving uncertain and vague data.
There are several well-known approaches to handling uncertainty during the clustering
process. There are such as a fuzzy theory [3], a rough set theory [4], vague sets [5], and interval
mathematics. But all of these theories have their inherent difficulties, as pointed out
in [6]. As a result, Molodstov proposed a novel theory to deal with the uncertainty that is called a
soft set theory [6]. It uses parameterization concept as its main vehicle, hence it offers wider
applications in real problems. At present, many researchers and scholars have contributed to
the development of soft set in theory as well as practice, including work of [7]–[16].
Clustering is the process of grouping objects based on information obtained from data
explaining the relationships between objects with principles to make the most of the similarity

TELKOMNIKA ISSN: 1693-6930 
A Soft Set-based Co-occurrence for Clustering Web User Transactions (Edi Sutoyo)
1345
between members of a group and minimize the similarity between groups. The goal is to find a
quality cluster in a decent time. The similarity of objects is usually derived from the proximity of
attribute values that describe data objects, whereas data objects are usually represented as a
point in a multidimensional space. Clustering can be used to identify areas that are dense,
group objects into groups that have homogeneous characteristics or variations of objects,
distinguish between one cluster and an another, and find the distribution and interesting
patterns between data attributes. In data mining, research focuses on the discovery methods for
clusters in large-scale databases effectively and efficiently [17]. The many clustering
approaches make it difficult to define universal quality measures. The many clustering
approaches make it difficult to determine global quality measures. However, some things to note
are the input parameters that do not complicate the user, the cluster of results that can be
analyzed, and scalability to the addition of dimension size and record dataset. Clustering is
another big issue of the soft set-based data analysis, particularly when it contains large and
imprecise data, e.g., clustering of web user transactions. Web user transaction data can
generally be obtained from the server log file. The server log is a log file created and managed
automatically by a server that serves to record all information from requests generated by users
with the right time along with the results of processing. A typical example is the web server log
that stores the page request history.
Web clustering is related to the extraction of knowledge from a web page, user session
or weblog data into some object groups [18]. The purpose of grouping web transactions into
some clusters is to gain a better understanding the behavior of the users or to segment web
visitors. One of the guidelines for optimizing the structure and navigation of a website can be
seen from the trend of visitor access patterns. To obtain visitor behavior information, analyzing
can be conducted on click pattern in clickstream website visitors. This can be obtained by
extracting information from the weblog data. Recently, De and Khrisna presented a rough set-
based algorithm for clustering web user transactions utilizing the similarity of upper
approximations [19]. However, high complexity is still an outstanding issue for finding the
similarity of upper approximations used to merger two or more clusters which have the same
similarity. To handle this issue, Yanto, et al. proposed a soft set-based framework for clustering
web user transactions [20]. Further, they proposed the RoCeT method for clustering web
transaction by using the notion of similarity class showing how to transactions are allocated in
the same cluster [21]. However, their technique still suffers from high computational complexity.
Therefore, in this work, we propose a soft set-based approach for clustering web user
transactions. To sum up, the main contribution of this work is listed as follows:
a. We propose a soft set approach for clustering web user transactions, which capable of
achieving lower computational complexity and also higher clustering purity.
b. Unlike rough set approach that uses similarity approach, the novelty of this approach uses a
co-occurrence approach of the soft set.
c. Also, this study presents comparison on theoretical analysis and performance results of the
proposed approach, and two rough set-based approaches are presented.
The rest of this paper is systematized as follows. Section 2 recalls the rudimentary
notion of rough set and soft set theory. Section 3 describes the proposed soft set-based
technique. Section 4 elaborates the experimental and comparison results. As a final point,
Section 5 concludes our works.
2. Theoretical Background
In this section, we discuss some rudimentary concepts of rough set theory and also soft
set theory.
2.1. Rough Set Theory
A 4-tuple (quadruple)  fVAUS ,,, is definition of information system, where
 U
uuuuU ,,,, 321  is a non-empty finite set of objects,  A
aaaaA ,,,, 321  is a non-
empty finite set of attributes,  Aa aVV 
 , aV is the domain (value set) of attribute a,
VAUf : is an information function such that   aVauf , , for every   AUau , ,
called information (knowledge) function. The rough set theory was initially developed by Pawlak

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[4] for modeling imprecision and granularity in an information systems. Rough set is established
on the assumption that with every object of the universe linked to some information (data,
knowledge). Objects are marked by information that cannot be distinguished (indiscernible) by
means of the information existing on the object. The indiscernibility relation produced in this way
is the basic mathematical theory of the rough set theory. The set of all indiscernible objects are
called the elementary set, and forms the basic granules (atom) of the knowledge of the
universe. If in the information system, there are at least two objects that have the same feature
then called indiscernible (indistinguishable).
Definition 2.1. Two objects Uyx , are considered to be B-indiscernible ( AB  in S)
if and only if    ayfaxf ,,  , for every Ba .
From Definition 2.1, it is clear that any subset of A generates its respective
indiscernibility relation. Furthermore, the relation is an equivalence relation, i.e. reflexive,
symmetric and transitive. Hence, the relation generates unique partition, let say BU/ and the
class containing an element x of U is represented by Bx . From such partition, we present the
ideas of lower and upper approximations of a subset, which are defined as follows.
Definition 2.2. (See [4].) The B-lower approximation of X symbolized by  XB and B-
upper approximations symbolized by  XB of X, are defined by:
    XxUxXB B
 and     XxUxXB B
 .
2.2. Soft Set Theory
Let U be a non-empty universe of objects, E is a set of parameters in relation to
objects of U ,  UP is the power set of U . The following is the definition of soft set theory.
Definition 3.1. (See [6].) A pair  EF, is called a soft set over U, where F is a mapping
given by  UPEF :
Meaning is to say, a soft set is a parameterized family of subsets of the universe U .
For E ,  F can be considered as the set of  -elements of the soft set  ,F E or as the set
of  -approximate elements of the soft set.
Example 2.1. Suppose we have a soft set  EF, describes the “cars being considered”
that Mr. Y is about to purchase. Assume that  1 2 3 4 5 6, , , , ,U c c c c c c and  54321 ,,,, eeeeeE  ,
for instance there are six cars in the universe U and E is car feature (a set of parameters), ie for
4,3,2,1i and 5, mean the parameters “expensive”, “sport car”, “family car”, “cheap”, and
“saving fuel”, respectively. Consider the mapping  UPEF : given by “car condition (.)”,
where (.) is to be filled in by one of the parameters Ee . Assume that    1 3 4,F e c c ,
   2 1 3, ,F e c c    3 2F e c ,    4 1 2 5, ,F e c c c , and    5 1 4 5, ,F e c c c . As from the example
above,  2eF means a car with “sport car” feature, whose functional value is the set  1 3,c c .
Therefore, the soft set  EF, can be presented as group of approximation as:
 
   
     
1 3 4 2 1 3
3 2 4 1 2 5 5 1 4 5
, , , ,
,
, , , , , ,
e c c e c c
F E
e c e c c c e c c c
   
  
    
.
In the following section, an alternative technique for clustering web user transactions
employing soft set theory is proposed. This alternative technique is expected to perform better
than previous rough set-based techniques in terms of two main concern, i.e. processing time
and also cluster purity, respectively. This method will also be proved mathematically to ensure
its performance.

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3. Proposed Soft Set-based Technique
This section, the soft set-based clustering for web user transactions is proposed. It is
based on the fact that user transactions can be represented as a soft set.
3.1. The Proposed Technique
Firstly, the relation of soft set theory and Boolean-valued information system is
described as follows.
Proposition 3.1. If  EF, is a soft set over the universe U, then  EF, is a binary-
valued information system   fVAUS ,,, 1,0
Proof. Let  EF, is soft set over the universe U, we define a mapping
 nfffF ,,, 11  where
iVUf :1 and  
 
 





eFx
eFx
xfi
,0
,1 1
, for ||1 Ai 
For that reason, if  Ae EVVEA 

1
, , where  1,01
eV then a soft set can be seen as
a Boolean-valued information system   0,1, , ,S U A V f .
From Proposition 3.1, a binary-valued information system can be easily represented as
a soft set. As a result, a one-to-one correspondence between  EF, over U and
  fVAUS ,,, 1,0 can be made. To illustrate Proposition 3.1, let we consider Example 2.1.
From the soft set in Example 2.1, Boolean-valued information system can be represented.
The representation of web user transactions using soft set theory is illustrated in the
Example 3.1 as follows.
Example 3.1. The data of web user transactions are taken from [19] given in Table 1.
This table contains four users  4U and five hyperlinks  5E .
Table 1. Representation Example 2.1 into soft set  EF,
 EU, 1e 2e 3e 4e 5e
1c 0 1 0 1 1
2c 0 0 1 1 0
3c 1 1 0 0 0
4c 1 0 0 0 1
5c 0 0 0 1 1
Table 2. Sample of Web User Transactions
AU / 1hl 2hl 3hl 4hl 5hl
1u 1 1 0 0 0
2u 0 1 1 1 0
3u 1 0 1 0 1
4u 0 1 1 0 1
Table 2 above represents whether the user clicks the hyperlink 1hl or the user clicks on
the hyperlink 2hl , and etc. The soft set representation of Table 2 is as follows.
 
   
   
  













435
244323
4212311
,
,,,,
,,,,,
,
uuhl
uhluuuhl
uuuhluuhl
EF

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From Proposition 3.1, the idea of similarity between two parameters (representing two
transactions) t and u in U is proposed in the following definition. Firstly, the idea of occurrence of
parameters in soft set theory is defined as follows.
Definition 3.1. Let  EF, be a soft set over the universe U representing data of web
user transactions and a web user transaction Uu . A parameter co-occurrence set of an
object ucan be defined as:
    1,:  eufEeucoo .
Clearly,     1:  efEeucoo . Definition 3.1 can be illustrated in the Example 3.2 as
follows.
Example 3.2. From soft set  EF, in Table 2, the parameter occurrence is defined as
follows:
   211 ,hlhlucoo 
   4322 ,, hlhlhlucoo 
   5313 ,, hlhlhlucoo 
   5324 ,, hlhlhlucoo  .
The following definition is from Definition 3.1.
user transactions and Uut , are two user transactions. The similarity between t and u denoted
by  utsim , is defined as follows:
     
   ucootcoo
ucootcoo
utsim


, .
From the similarity definition above, it can be concluded that    1,0, utsim . The
  1, utsim , when two transactions t and s are precisely the same. Meanwhile,   0, utsim , if
two transactions t and s does not the same items in common.
The representation of the Definition 3.2 is in the next example.
Example 3.3. From soft set  EF, in Table 2 and Example 3.2, the similarity between
two user transactions is given as follows:
     
   
   
   
 
 
25.0
,,,
,,,
,,,
,
4321
2
43221
43221
21
21
21



hlhlhlhl
hl
hlhlhlhlhl
hlhlhlhlhl
ucooucoo
ucooucoo
uusim




     
   
   
   
 
 
25.0
,,,
,,,
,,,
,
5321
1
53121
53121
31
31
31



hlhlhlhl
hl
hlhlhlhlhl
hlhlhlhlhl
ucooucoo
ucooucoo
uusim




and etc.

1349
From Definition 2.1, soft set theory can be referred as a binary relation. Furthermore,
from Definition 3.2, we present the notion a binary relation with respect to the similarity between
two user transactions.
user transactions and Uut , are two user transactions. A binary relation R between t and u
denoted by tRuis defined as follows
  th, utsim
where  1,0th is a user pre-defined threshold value.
This relation R in Definition 3.3 is both reflexive and symmetric, but may not a transitive.
The representation of the Definition 3.3 is in the next example.
Example 3.4. From soft set  EF, in Table 2 and Example 3.3, the following binary
relations are formed with a given threshold 0.4
42 Ruu since    
 
4.05.0
,,,
,
,
5432
42
42 
hlhlhlhl
hlhl
uusim
and
43 Ruu since    
 
4.05.0
,,,
,
,
5321
53
43 
hlhlhlhl
hlhl
uusim .
From Definition 3.3, a similarity class can be defined as follows.
user transactions and a web user transaction u U .The similarity class of t, denoted by  uSC ,
is defined as a set of transactions which are similar to t i.e.
   tRuTutSC : .
From Definition 3.4, for the given any threshold values, we can also get any similarity
classes. An expert can choose a threshold based on their preferable value to get expected
similarity classes. The representation of the Definition 3.4 is in the following example.
Example 3.5. From soft set  EF, in Table 2, we the following similarity classes of
each transaction with a given threshold 0.4
   11 uuSC  ,    422 ,uuuSC  ,    433 ,uuuSC  , and    4324 ,, uuuuSC  .
3.2. Correctness Proof
The following definition states that two web user clusters in U to be similar if their
union are equal.
user transactions. Two web user clusters iC and jC in U , for ji  are said to be the same if
  ii uSCC  , for Ui ,,2,1  .
From similarity classes in Definitions 3.4 and 3.5, we can form a cluster of web user
transactions as shown in Proposition 3.2.
Proposition 3.2. Let  EF, be a soft set over the universe U representing data of web
user transactions and  iuSC be a similarity class of transaction u, for Ui ,,2,1  . If
   iuSC , then   ii CuSC  .
Proof. We suppose that   ii CuSC  , then from Definition 3.5, we have ji CC  and
further ji CC  . The consequence, we get the following:

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        ji uCuC
  iuC
This is a contradiction from the hypothesis.
3.3. Algorithm and Its Complexity
The algorithm of the proposed technique is presented in Figure 1.
Algorithm: Soft set technique
Input: Web user transactions data set
Output: Web user transactions clusters
Begin
Step 1. Calculate the degree of the similarity between two object transactions.
Step 2. Get the similarity class with the given threshold value.
Step 3. Combine the transaction if there is two of similarities have a non-empty
intersection.
End
Figure 1. The pseudo-code of the soft set-based web user transactions
From Step 3 in Figure 1, the clusters formed are based on a non-void intersection of the
two similarity classes, i.e.
       iii uSCuSCC .
From the proposed technique, suppose that there are n objects in a soft set  EF, over
the universe U representing data of web user transactions. As a result, there are at most n
similar classes. For getting this done, the technique needed is
2
2
n
computation for determining
the similarity matrix. Since the computation of union of relation similarity matrix to obtain the
cluster is
2
2
n
. Accordingly, the computing complexity as a whole is polynomial  2
On .
Table 3. Complexity Comparison
De & Krishna [27] Yanto et al. [28], [29] Proposed Technique
Complexity
 nn 22 2
O   2
2O n  2
On
Based on Table 3, the proposed approach achieves lower complexity as compared to
others.
4. Results and Discussion
The experimental results of the clustering web user transactions technique are
elaborated in this section. To compare the proposed technique and techniques proposed by
[19]–[21] are carried out on a 1.86 GHz Intel Core i3-3217U machine with 8 GB memory using
Windows 10 operating system. The techniques for clustering web transactions are implemented
in MATLAB 8.4 (R2014b). For experiment test, the two UCI Repository of Machine Learning
Databases benchmark datasets are used. Those datasets are obtained from [22]. This data only
contains the server-side logs because the data from client-side is not recorded. This

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experiments use 2000 data transactions, and then those data are split into five different sample
size groups i.e.100, 200, 500, 1000, and 2000 data transactions, respectively.
4.1. Cluster Purity
In general terms, web user transactions clustering algorithms are based on criteria to
assess the quality of a given class. Especially, they take some parameters as an input, e.g.
number of classes. Since the clustering algorithms are an apriori technique, then they need to
be assessed in term of the purity of classes [44]. Formally, the purity of classes (clusters) is
defined as follows:
 


n
it
t
t
i h
Purity ,
where  hitt is the number of data occurring in both the i-th cluster under the given
threshold and  nt is the number of data in the dataset. Meanwhile, the overall purity of
clusters is defined as follows:
 
 
clusterof#
Purity
PurityOverall
clusterof#
1

 i
i
i
In accordance with the above equations, the highest value of overall class purity reflects
the best clustering result, where perfect clustering results are closing to have a value of 100 %.
In the next sub-section, we elaborate the experimental results of our proposed soft set-based
technique employing the benchmark datasets.
4.2. Msnbc.com Dataset
This msnbc.com dataset describes the pages of websites visited by visitors. The data is
recorded at the level URLs category in chronological order taken from the Internet Information
Server (IIS) server log file from the msnbc.com website. Each line of the dataset corresponds to
a request from a user for a web page.
Table 4 shows the comparative results in terms of execution time (in seconds) and
cluster purity on each number of different data samples.
Table 4. Performance Comparison of Msnbc.com data set
Number
of
Transacto
ns
Executing Time Clusters Purity
Technique
[27]
Technique
[28], [29]
Proposed
Improve
ment
Techniqe
[27]
Techniqe
[28], [29]
Proposed Improvement
100 15.6 9.8 5.9 115.3% 93.0% 100% 100% 3.5%
200 171.2 121.2 65.9 121.9% 96.0% 100% 100% 2.0%
500 819.6 493.7 259.1 153.4% 95.5% 100% 100% 2.3%
1000 3723.6 2092.9 1283.9 126.5% 95.5% 100% 100% 2.3%
2000 5371.2 4352.8 2901.8 67.6% 96.9% 100% 100% 1.6%
Average improvement 116.9% Average improvement 2.3%
Based on the results shown in Table 4, the rough set-based approaches proposed by
[19]–[21] took longer processing time, because to find the similarity of upper approximations
requires many iterations. Meanwhile, the soft set-based approach shows significant
improvement of more than 116 % for user transactions starting from 100 until 2000 data sample.
For cluster purity, the proposed approach improves up to 2.3% as compared to two rough set-
based approaches.

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4.3. Microsoft.com data set
This dataset describes the pages visited by users who visit www.microsoft.com. For
each user, the data lists all areas of the website (Vroot) that a user visits within a week. The log
files do not contain personally identifiable information, and the title and also URL identifies the
Vroots.
Table 5. Performance comparison of Microsoft.com data set
Number
of
Transacti
ons
Executing Time Clusters Purity
Technique
[27]
Technique
[28], [29]
Propose
d
Improve
ment
Techniqu
e
[27]
Technique
[28], [29]
Proposed Improvement
100 12.1 6.4 4.1 125.6% 76.0% 100% 100% 12.0%
200 51.1 32.1 19.3 115.5% 79.5% 100% 100% 10.3%
500 431.7 215.9 173.9 86.2% 87.4% 100% 100% 6.3%
1000 2375.8 1598.4 1079.1 84.2% 91.5% 100% 100% 4.3%
2000 4751.6 2375.8 1663.1 114.3% 93.2% 100% 100% 3.4%
Average improvement 105.2% Average improvement 7.2%
Table 5 shows the comparison of the processing time (in second) and clusters purity.
As we can see that, the proposed approach has shown improvement of more than 105% in
terms of execution time for user transactions starting from 100 until 2000. For cluster purity, the
proposed approach improves up to 7.2% from the two rough set-based approaches.
5. Conclusion
In this paper, we have examined the clustering web user transactions which focusing on
reducing computational complexity and increasing cluster purity. The proposed method is the
first study that has proposed for clustering web user transactions by using soft set theory. We
proposed an algorithm with varying lower computational complexity and higher cluster purity.
Although several existed baseline techniques address the issues concerning web user
transactions clustering, none of these techniques provide low computational complexity and
high cluster purity. We have carried out a comparative analysis of the proposed technique
concerning final computation complexity and cluster purity. The results showed that the
proposed technique outperforms two rough set-based techniques on computation complexity
and cluster purity.
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