Publication Repository
SEMANTIC WEB MINING ON TOPIC MAP USING GALOIS LATTICE
Gunawan *, Lukman Zaman PCSW †, Tri Kurniawan Wijaya ††, Novieana Dewi Sugianto †††
* Electrical Engineering Department, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember
Kampus ITS Keputih, Sukolilo, Surabaya 60111, Indonesia
† Computer Science Department, Sekolah Tinggi Teknik Surabaya
Ngagel Jaya Tengah 73-77, Surabaya 60284, Indonesia
email: admin@hansmichael.com*, lz@stts.edu †, tritritri@stts.edu ††, v134n4@yahoo.com †††
ABSTRACT
The most challenging problem of internet technologies
for future decade is how to save and arrange information
in the web. Semantic web which was thought by Tim
Berners-Lee provides framework to fulfill this
requirement. Semantic web idea itself is to make the web
more effective, so that the information can be accessed by
machines, not only humans.
This research will discuss web mining on one of the
semantic structures, XML Topic Map. The methods which
will be used to mine XML Topic Map are conceptual
classification,
characterization,
and
clustering.
Classification based on Formal Concept Analysis (FCA)
and Galois connection. Galois lattice will group
information as objects and make the connection between
that information more semantic. Characterization consists
of statistic calculation of every object. It is used to define
the object profiles. The object profiles will be used as a
model for topic map filtering. The clustering process is
based on Galois lattice concept and will be used to
generate cluster tree.
Keywords: Semantic Web, Formal Concept Analysis,
Galois Lattice, Conceptual Classification, Clustering,
Characterization.
1
INTRODUCTION
Recently, there are many websites and web-based
applications. Web has a lot of information, unfortunately
they are unstructured. Therefore, it is difficult to collect
and understand the information within. Recent methods in
web engineering are now developing a web application
that is "separated" from conceptual model. This idea
makes integration of different web applications more
difficult.
It is important to build the technical framework in
which applications and data functions can be represented
between the different web applications. Semantic web
provides the appropriate framework to meet this purpose.
Semantic web is a “vision” to define the data on the web
and connects the data each other with a way that can be
used by an engine in different applications. In other
words, semantic web allows more cooperation between
computer and user.
An example of the semantic web is XML topic map. A
topic map illustrates the structure of knowledge and
connecting it with the source of information. In addition,
the topic map can be developed to help users find relevant
information. Topic map is designed to handle organization
and navigation issue of large information.
One of the mining process on the topic map is done by
classification, characterization, cleaning up the data
(through a definition of a profile), and clustering.
Classification is based on Formal Concept Analysis (FCA)
and Galois lattice algorithm. Characterization will
conclude a profile and evaluate the relevant information.
Clustering will improve the web navigation through
related topics and then displayed in topics level based on
the user requirements.
2
2.1
THEORY, ANALYSIS, DESIGN, AND
IMPLEMENTATION
Semantic Web
Semantic web is a collection of information that is
connected to each other in a way that easily processed by
machines. Semantic Web will become an efficient way in
representing data on the World Wide Web, or act as a
database that is connected with the links globally.
In general, the data/information that is stored on the
web in the HTML file, is useful for a context, but can not
be used for another context. The problem is that the data
now would be difficult to use in large numbers, as there is
no global system to determine how to publish the data so
that it can be processed easily by everyone, for example:
information about local sporting events, weather
information, statistics League Baseball, and television.
This information is displayed in many sites, but all of
them in the form of HTML. The problem faced is that in
some circumstances, it is difficult to use the data in a way
that is desired by someone.
Therefore the semantic web can be viewed as a major
solution technique. Using semantic web, it will become
easier to publish data in a form that can be used for any
other purposes.
2.2
Topic Map
Topic map is a new ISO standard to describe the
structure of knowledge and connecting it with the source
of information. In other words topic map is a technique
that allows for knowledge management.
The basic concept of a topic map is: topic, association,
and occurrence.
Topic is the concept and the most fundamental part in
a topic map. Topic has three kinds of characteristics,
including names, occurrences, and roles in associations. A
topic can be categorized based on its type.
An association is a relationship between two or more
topic. Association between the topics can also be grouped
according to type. Types of association are important part
because they are a source of determining whether it was
connected to the source of the information or not.
Occurrence is one or more sources of relevant
information and connected with a topic in several ways.
Occurrence in general is extern to the topic map document
itself. An occurrence can be a monograph, which is
provided for a specific topic, or an article on the topic in
an encyclopedia. Occurrence may also be a picture or
video that describes the topic, a comment about the topic,
some form or another source where the information will
be relevant to the subject in question.
The principle of the formation of a topic map
applications in an distributed information system is to
organize knowledge, information and data from one or
more sources, and do so in a way that meets the user
requirements. Some applications that can be applied using
a topic map are: 1) information systems and business
process information flows, 2) knowledge management
systems, 3) intranets, 4) extranets, 5) portals and content
of the source, 6) commercial information services, 7)
document management systems, and 8) system
documentation.
2.3
Galois Lattice and Mining Topic Map
Topic map as one of the structure of semantic web will
make the mining process more efficient. The process is
shown in figure 1. The goal of the mining process on the
topic map is to assist users in finding relevant information
which can be made in three ways as follow:
1. Evaluating the web site relevant to the user
requirements based on semantic criteria.
2. Filter the topic map to find the main subject and to
discard the less relevant topic.
3. Increasing the web navigation through the topicrelated concept and then do some visualization
through different level of detail.
that provides information. FCA will be used for the
conceptual clustering. There are two terms that need to be
notice: an object is a topic from the topic or association
map and properties is the characteristics of the object.
Figure 1. Web mining process on Topic Map
The first stage of the classification is form a new
object and property. If there is an element that has an
identifier, the new object is created. Meanwhile, the object
properties associated with the object attribute value.
Properties will be given a weight based on the level of the
significance. The formation of objects and properties in
the first stage is shown in figure 2.
Figure 2. Formation of the object and property of first step
2.3.1 Classification
The first step of the process is a conceptual
classification algorithm based on Formal Concept
Analysis (FCA) and the Galois Connection. FCA is a
mathematical approach to the analysis of the data structure
Weight of each property depends on the attributes
interests in the topic map. The more important the
attribute in the existence of the topic map, the greater the
value of the weight will be.
The second phase is to add non-intrinsic properties by
crossing the data. For an object O with a set of property P,
each property P will be an object together with O as the
property. Object’s properties are intrinsic properties. All
the properties which are added from recursive process are
also intrinsic properties. The establishment of the basic
object and property in the second stage is shown in figure
3.
In Galois lattice only pairs which are maximally
widened is maintained in a hierarchy. Maximum
expansion set idea established by the idea of a
mathematical equation (closure) in the ordered set.
Equation on the ordered set (E, =) on its applications
h:EÆE has the following requirements:
1. ∀x ∀y, x=y ⇒ h(x)=h(y)
2. ∀x, h(x)=x
3. ∀x, h(h(x))=h(x)
Figure 3. Formation of the object and property of second step
In the third stage, objects are grouped based on the
existing Galois connection. Given two sets E and E’ (E
contains a collection of objects and E’ is the set of object
properties) and a binary relation R⊆ExE’ between these
two sets. P(E) is the powerset of E and P(E’) is the
powerset of E’. Individual elements in lattice are a partner,
also called the concept and symbolized with (X, X’). A
concept formed from two set X ∈ P(E) and X’ ∈ P(E’)
such as:
X’=f(X)
where f(X)={x’∈E’| ∀x∈X,xRx’}
X=f’(X’)
where f’(X’)={x∈E|∀x’∈X’,xRx’}
Partial order in concept defined as follows:
If C1=(X1,X’1) and C2=(X2,X’2),
C1 1 DO
4 Lk+1 := ∅
5 FOR ALL combination of pairs (X ,X’) and (Y, Y’)
in Lk DO
6 Z’ := X’ ∩ Y’
7 IF Z’≠ ∅ THEN
8
IF there is a pair(Z,Z’)∈Lk+1 THEN
9
Z := Z ∪ Y
10
ELSE
11
Lk+1:=Lk+1∪{X∪Y,Z}
12
END IF
[marking G pair]
13
IF Z’ = X’ THEN
14
mark (X, X’) in Lk
15
END IF
16
IF Z’ = Y’ THEN
17
mark (Y, Y’) in Lk
18
END IF
19 END IF
20 END FOR
21 k := k + 1
22 END WHILE
Hasse diagram algorithm is proposed by Alaoui [1]
who improved the Chein algorithm by adding a link
between the pair using structures of the level. Algorithm
which is formed Hasse diagram is shown in algorithm 2.
Algorithm 2. Build Hasse Diagram
[Algorithm to build the Hasse Diagram from the lattice
pair. Building Hasse diagram also considered whether one
is the part of another pair]
1 FOR each level from 1 to last level DO
2 FOR each non marked pair (X,X’) of Li DO
3 FOR each non marked pair (Y,Y’) of Li+1 DO
4
IF Y’ ⊂ X’ THEN
5
(X,X’) is a child of (Y,Y’)
6
END IF
7 END FOR
8 END FOR
9 END FOR
In algorithm 2, Hasse diagram is formed through
iterations by considering the pair G level 1 until the last
level. G pair which is used to form the Hasse diagram is
the pair which is not marked.
2.3.2 Characterization
Characterization of the topic map uses statistical
calculations of each object. It is aimed to conclude a
profile for the object. Statistical calculations based on the
weight of each object in the topic map.
An object O is characterized by the vector with 6
components (A1…A6). The six components are defined
as follows:
• A1: percentage concept of sub-lattice where objects
appear in the list of extensions.
• A1: the maximum number of objects where O is
grouped divided by the total of all objects.
• A3: the average number of objects where O is
grouped divided by the total of all objects.
• A4: the maximum number of O’s properties that are
used together with the object that is contained in S
(the collection of objects that are grouped with an O
in one or more of the concept lattice), divided by the
total of all objects.
• A5: the average number of O’s properties that are
used together with other objects, divided by the total
of all properties.
• A6: the number of occurrence of the object in the
topic map divided by the number of occurrence of
the object with the same type (topic or association).
After the statistics are calculated for each topic and
association, the object profile can be concluded. For N
object, O1, O2, … ON, each component Ai for profile
vector P is calculated as in the equation:
N
P. Ai = ∑ Oj. Ai * Oj. A6
(1)
j =1
(where Oj.Ai is the component Ai on object j.)
Objects that are most relevant (regular object), which
has many properties of many other objects will be
maintained. Regular Objects are more important by the
means of semantic compared with another objects.
The object which is regular is proved using the
following conditions:
O.A1 ≥ Profile.A1
O.A2 ≥ Profile.A2
Condition is improved by adding a standard deviation.
Calculation of standard deviation is:
N
∑ | O .A
j
Std .dev. A3 =
3
j =1
N
− P. A3 |
(2)
Regular conditions can be changed using a coefficient
C. Relation of the objects with regular coefficients C and
the standard deviation is defined as follows:
O.A1 + C x std.dev.A1 ≥ P.A1
O.A2 + C x std.dev.A2 ≥ P.A2
Characterization phase will produce a list of regular
items that are stable, where the topic map has been filtered
to eliminate non-regular objects (objects that are less
semantic). After this stage, there will be a new list of
objects that are used as an input to Galois classification
algorithm. Lattice then formed and the new statistics are
calculated on the new object to create the new profile, and
so forth until all items become regular.
2.3.3 Clustering
The next step after characterization is clustering.
Clustering is based on the concept of Galois conceptual
classification, which was developed using cluster tree.
Elections of the father of a concept based on the
following hierarchy criteria:
1. First, based on the distance of each father with the
lower bound of the lattice. Distance is related to the
amount of edge between the father and the lower bound of
the lattice.
2. If the distance of a father of a node with the lower
bound of the lattice is smaller than the other nodes, then
the node is selected. The closer the distance from the
lower bound of the lattice, the more semantic the concept
is.
3. If there are multiple nodes on the minimum distance
from the lower bound of the lattice, the amount of its
properties’ weight which is contained in their intention are
then compared. Node with the highest weight is selected.
4. If several fathers meet criteria-3, then choose ones
that minimize the total number of branches in the tree.
5. If the criteria-4 has not been fulfilled, then several
trees were built based on several possible fathers.
Some other criteria that are required can be counted
from a cluster tree, such as lattice initial concept that is
not selected for clustering process. In addition, level of the
navigation, the distance between objects, and the
similarity between objects can be analyzed. Depth of the
tree shows the number of tree-level navigation is provided
for the user. Cluster distribution at each level of separation
can also provide important information for the user. If a
cluster does not have a father, it means that it can not be
generalized. In addition, the cluster that does not have any
children means that its level is the most specific level.
The distance between two clusters is average or
maximum or minimum distance between two objects (one
object in each cluster). O1 and O2 given as two objects,
P1 is a collection of properties owned by O1, whereas P2
is a collection of properties owned by O2. INTER also
given as slices of P1 and P2, and the UNION as a
combination of P1 and P2. The similarity of object O1 and
O2 can be calculated as in the equation:
card ( INTER )
S (O1, O 2) =
∑ wi
i =1
card (UNION )
∑ w' j
whereas the distance O1 and O2 is defined as follow:
3
1
S (O1, O 2)
Table 2. Characterization results
Statistics
(A1... A6)
Other
information
Testing is done on an XML topic map. Table 1 shows
the results of the classification.
Section A
(Coefficient
C=1.12)
Object 0
A1=0.10563
A2=0.28571
A3=0.08761
A4=0.08571
A5=0.32
A6=0.0
…
#iter=5
%object left=20
#regular object = 10
Section B
(Coefficient
C=1.18)
Object 0
A1=0.10204
A2=0.32432
A3=0.08648
A4=0.08108
A5=0.32
A6=0.0
…
#iter=5
%object left=58
#regular object =27
Table 2 shows that in general, the statistics on the
value of section A is larger when compared with the value
of statistics on the section B. Section A and The number
of objects left in section B is more than the number of
objects left in section A, shows that the filtering level is
different. Greater value of the coefficient gives larger
restrictions for the regular object, consequently the less
the number of objects that eliminated.
The results of clustering process can be seen in table 3.
We also used two different coefficient values.
Table 3. Clustering results
Cluster
Analysis
(4)
TESTING
Result
#object=42
#properties=42
#object=34
#properties=34
In characterization phase we used two different values
of coefficients to filter the same topic map. Sample results
of the characterization are shown in table 2.
(3)
j =1
D(O1, O 2) = 100 −
Table 1. Classification results
Process
Object dan property
establishment
Galois connection
Other
information
Section A
(Coefficient C=1.12)
between Obj1 &
Obj2
similarity: 0.28571
distance: 96.5
…
#level=4
#cluster=10
Section B
(Coefficient C=1.18)
between Obj1 &
Obj2
similarity: 0.5
distance: 98.0
…
#level=4
#cluster=38
Table 3 shows that the smaller the value of coefficient
C the more objects are grouped into a cluster. The higher
the level of the cluster then the more specific
object/cluster, the lower the level of the cluster the objects
are more general.
4
CONCLUSION AND FUTURE WORK
In this research we implement a semantic web mining
on the topic map and then test it to an XML topic map.
XML topic map as one of the structure of semantic web
data is able to show the data of the web more structured
than before. Therefore using the XML topic map, mining
on the web will become easier. Conceptual classification
stage evaluate topic map and display it in the form of
objects and properties. In addition, establishment of the
object and properties must be object oriented. The Galois
connection indicates the generalization/specialization
relations of the topic map objects. The object which has
many properties is more specific than other object which
has a few properties. Characterization topic map filter the
data in topic map. Filtering is used to eliminate the data
that is not relevant enough. The number of data eliminated
depends on the value of coefficient (C), the greater the
value of the coefficient, then the less the number of the
data that are eliminated. Clustering topic map shows the
topic map data in the different levels, indicating the
generalization/specialization data cluster.
Based on our testing results, we recommended the
following for further development: 1) Use several XML
topic map to ensure the results of our mining process 2)
Form more detail cluster representations, show that some
cluster are more relevant than others, and display more
detailed information of the cluster 3) develop semantic
web mining using another semantic structure, such as
XML and RDF.
REFERENCE
[1]
[2]
[3]
Alaoui, H., Algorithmes de Manipulation du Treillis
de
Galois
d'une
Relation
Binaire
et
Applications.Masters Thesis, Université du Québec
à Montréal, 1992.
Berners-Lee,Tim, Hendler, James, dan Lassila,Ora,
The Semantic Web, Scientific American Inc, 2001.
Bharat, K. dan Broder, A., A technique for
measuring the relative size and overlap of public
Web search engine. In 7th Int. WWW Conf
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[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
Carpineto, C., Romano, G., Galois: An ordertheoretic approach to conceptual clustering, Proc. Of
the 10th Conference on Machine Learning, Amherst,
MA, Kaufmann, 1993.
Chein, M., Algorithme de Recherche des SousMatrices Premières d'une Matrice. Bull, Math. Soc.
Sci.Math. R.S. Roumanie, 1969.
Davey, B. A. dan Priestley, H. A,. Introduction to
Lattices and Order, Cambridge: Cambridge
University Press, 1992.
Grand, Benedicte Le, Michel Soto, XML Topic Map
and
Semantic
Web
Mining,
Laboratoire
d'Informatique de Paris 6, 2002.
Godin, R, Chau, T.-T., Incremental concept
formation
algorithms
based
on
Galois
Lattices,Computational intelligence, 1998.
Harmelen, F. dan Fensel, D., Practical Knowledge
Representation for the Web, IJCAI, 1999.
International Organization for Standardization,
ISO/IEC 13250, Information Technology-SGML
Applications-Topic Maps, Geneva: ISO, 1998
Malgrange, Y. ,Proceedings of the Deuxième
Congrès de l'AFCALTI,Gauthier-Villars, 1992.
Perkowitz, M. dan O. Etzioni,O., Adaptive Web
sites: an AI challenge, In IJCAI,1997
Thuraisingham,Bhavani, Web Data Mining and
Applications in Business Intelligence and CounterTerrorism, 2003
TopicMaps.Org XTM Authoring Group, XTM:
XML Topic Maps (XTM) 1.0: TopicMaps.Org
Specification, 3 March 2001.
Wille, R., Restructuring Lattice Theory: an
Approach Based on Hierarchies of Concepts, In I.
Rival(Eds.), 1982.
Wolf, Karl Erich, A First Course in Formal Concept
Analysis, 1994.
World Wide Web Consortium, Resource Description
Framework (RDF) Model and Syntax Specification,
W3C Recommendation, 22 February 1999.
Gunawan *, Lukman Zaman PCSW †, Tri Kurniawan Wijaya ††, Novieana Dewi Sugianto †††
* Electrical Engineering Department, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember
Kampus ITS Keputih, Sukolilo, Surabaya 60111, Indonesia
† Computer Science Department, Sekolah Tinggi Teknik Surabaya
Ngagel Jaya Tengah 73-77, Surabaya 60284, Indonesia
email: admin@hansmichael.com*, lz@stts.edu †, tritritri@stts.edu ††, v134n4@yahoo.com †††
ABSTRACT
The most challenging problem of internet technologies
for future decade is how to save and arrange information
in the web. Semantic web which was thought by Tim
Berners-Lee provides framework to fulfill this
requirement. Semantic web idea itself is to make the web
more effective, so that the information can be accessed by
machines, not only humans.
This research will discuss web mining on one of the
semantic structures, XML Topic Map. The methods which
will be used to mine XML Topic Map are conceptual
classification,
characterization,
and
clustering.
Classification based on Formal Concept Analysis (FCA)
and Galois connection. Galois lattice will group
information as objects and make the connection between
that information more semantic. Characterization consists
of statistic calculation of every object. It is used to define
the object profiles. The object profiles will be used as a
model for topic map filtering. The clustering process is
based on Galois lattice concept and will be used to
generate cluster tree.
Keywords: Semantic Web, Formal Concept Analysis,
Galois Lattice, Conceptual Classification, Clustering,
Characterization.
1
INTRODUCTION
Recently, there are many websites and web-based
applications. Web has a lot of information, unfortunately
they are unstructured. Therefore, it is difficult to collect
and understand the information within. Recent methods in
web engineering are now developing a web application
that is "separated" from conceptual model. This idea
makes integration of different web applications more
difficult.
It is important to build the technical framework in
which applications and data functions can be represented
between the different web applications. Semantic web
provides the appropriate framework to meet this purpose.
Semantic web is a “vision” to define the data on the web
and connects the data each other with a way that can be
used by an engine in different applications. In other
words, semantic web allows more cooperation between
computer and user.
An example of the semantic web is XML topic map. A
topic map illustrates the structure of knowledge and
connecting it with the source of information. In addition,
the topic map can be developed to help users find relevant
information. Topic map is designed to handle organization
and navigation issue of large information.
One of the mining process on the topic map is done by
classification, characterization, cleaning up the data
(through a definition of a profile), and clustering.
Classification is based on Formal Concept Analysis (FCA)
and Galois lattice algorithm. Characterization will
conclude a profile and evaluate the relevant information.
Clustering will improve the web navigation through
related topics and then displayed in topics level based on
the user requirements.
2
2.1
THEORY, ANALYSIS, DESIGN, AND
IMPLEMENTATION
Semantic Web
Semantic web is a collection of information that is
connected to each other in a way that easily processed by
machines. Semantic Web will become an efficient way in
representing data on the World Wide Web, or act as a
database that is connected with the links globally.
In general, the data/information that is stored on the
web in the HTML file, is useful for a context, but can not
be used for another context. The problem is that the data
now would be difficult to use in large numbers, as there is
no global system to determine how to publish the data so
that it can be processed easily by everyone, for example:
information about local sporting events, weather
information, statistics League Baseball, and television.
This information is displayed in many sites, but all of
them in the form of HTML. The problem faced is that in
some circumstances, it is difficult to use the data in a way
that is desired by someone.
Therefore the semantic web can be viewed as a major
solution technique. Using semantic web, it will become
easier to publish data in a form that can be used for any
other purposes.
2.2
Topic Map
Topic map is a new ISO standard to describe the
structure of knowledge and connecting it with the source
of information. In other words topic map is a technique
that allows for knowledge management.
The basic concept of a topic map is: topic, association,
and occurrence.
Topic is the concept and the most fundamental part in
a topic map. Topic has three kinds of characteristics,
including names, occurrences, and roles in associations. A
topic can be categorized based on its type.
An association is a relationship between two or more
topic. Association between the topics can also be grouped
according to type. Types of association are important part
because they are a source of determining whether it was
connected to the source of the information or not.
Occurrence is one or more sources of relevant
information and connected with a topic in several ways.
Occurrence in general is extern to the topic map document
itself. An occurrence can be a monograph, which is
provided for a specific topic, or an article on the topic in
an encyclopedia. Occurrence may also be a picture or
video that describes the topic, a comment about the topic,
some form or another source where the information will
be relevant to the subject in question.
The principle of the formation of a topic map
applications in an distributed information system is to
organize knowledge, information and data from one or
more sources, and do so in a way that meets the user
requirements. Some applications that can be applied using
a topic map are: 1) information systems and business
process information flows, 2) knowledge management
systems, 3) intranets, 4) extranets, 5) portals and content
of the source, 6) commercial information services, 7)
document management systems, and 8) system
documentation.
2.3
Galois Lattice and Mining Topic Map
Topic map as one of the structure of semantic web will
make the mining process more efficient. The process is
shown in figure 1. The goal of the mining process on the
topic map is to assist users in finding relevant information
which can be made in three ways as follow:
1. Evaluating the web site relevant to the user
requirements based on semantic criteria.
2. Filter the topic map to find the main subject and to
discard the less relevant topic.
3. Increasing the web navigation through the topicrelated concept and then do some visualization
through different level of detail.
that provides information. FCA will be used for the
conceptual clustering. There are two terms that need to be
notice: an object is a topic from the topic or association
map and properties is the characteristics of the object.
Figure 1. Web mining process on Topic Map
The first stage of the classification is form a new
object and property. If there is an element that has an
identifier, the new object is created. Meanwhile, the object
properties associated with the object attribute value.
Properties will be given a weight based on the level of the
significance. The formation of objects and properties in
the first stage is shown in figure 2.
Figure 2. Formation of the object and property of first step
2.3.1 Classification
The first step of the process is a conceptual
classification algorithm based on Formal Concept
Analysis (FCA) and the Galois Connection. FCA is a
mathematical approach to the analysis of the data structure
Weight of each property depends on the attributes
interests in the topic map. The more important the
attribute in the existence of the topic map, the greater the
value of the weight will be.
The second phase is to add non-intrinsic properties by
crossing the data. For an object O with a set of property P,
each property P will be an object together with O as the
property. Object’s properties are intrinsic properties. All
the properties which are added from recursive process are
also intrinsic properties. The establishment of the basic
object and property in the second stage is shown in figure
3.
In Galois lattice only pairs which are maximally
widened is maintained in a hierarchy. Maximum
expansion set idea established by the idea of a
mathematical equation (closure) in the ordered set.
Equation on the ordered set (E, =) on its applications
h:EÆE has the following requirements:
1. ∀x ∀y, x=y ⇒ h(x)=h(y)
2. ∀x, h(x)=x
3. ∀x, h(h(x))=h(x)
Figure 3. Formation of the object and property of second step
In the third stage, objects are grouped based on the
existing Galois connection. Given two sets E and E’ (E
contains a collection of objects and E’ is the set of object
properties) and a binary relation R⊆ExE’ between these
two sets. P(E) is the powerset of E and P(E’) is the
powerset of E’. Individual elements in lattice are a partner,
also called the concept and symbolized with (X, X’). A
concept formed from two set X ∈ P(E) and X’ ∈ P(E’)
such as:
X’=f(X)
where f(X)={x’∈E’| ∀x∈X,xRx’}
X=f’(X’)
where f’(X’)={x∈E|∀x’∈X’,xRx’}
Partial order in concept defined as follows:
If C1=(X1,X’1) and C2=(X2,X’2),
C1 1 DO
4 Lk+1 := ∅
5 FOR ALL combination of pairs (X ,X’) and (Y, Y’)
in Lk DO
6 Z’ := X’ ∩ Y’
7 IF Z’≠ ∅ THEN
8
IF there is a pair(Z,Z’)∈Lk+1 THEN
9
Z := Z ∪ Y
10
ELSE
11
Lk+1:=Lk+1∪{X∪Y,Z}
12
END IF
[marking G pair]
13
IF Z’ = X’ THEN
14
mark (X, X’) in Lk
15
END IF
16
IF Z’ = Y’ THEN
17
mark (Y, Y’) in Lk
18
END IF
19 END IF
20 END FOR
21 k := k + 1
22 END WHILE
Hasse diagram algorithm is proposed by Alaoui [1]
who improved the Chein algorithm by adding a link
between the pair using structures of the level. Algorithm
which is formed Hasse diagram is shown in algorithm 2.
Algorithm 2. Build Hasse Diagram
[Algorithm to build the Hasse Diagram from the lattice
pair. Building Hasse diagram also considered whether one
is the part of another pair]
1 FOR each level from 1 to last level DO
2 FOR each non marked pair (X,X’) of Li DO
3 FOR each non marked pair (Y,Y’) of Li+1 DO
4
IF Y’ ⊂ X’ THEN
5
(X,X’) is a child of (Y,Y’)
6
END IF
7 END FOR
8 END FOR
9 END FOR
In algorithm 2, Hasse diagram is formed through
iterations by considering the pair G level 1 until the last
level. G pair which is used to form the Hasse diagram is
the pair which is not marked.
2.3.2 Characterization
Characterization of the topic map uses statistical
calculations of each object. It is aimed to conclude a
profile for the object. Statistical calculations based on the
weight of each object in the topic map.
An object O is characterized by the vector with 6
components (A1…A6). The six components are defined
as follows:
• A1: percentage concept of sub-lattice where objects
appear in the list of extensions.
• A1: the maximum number of objects where O is
grouped divided by the total of all objects.
• A3: the average number of objects where O is
grouped divided by the total of all objects.
• A4: the maximum number of O’s properties that are
used together with the object that is contained in S
(the collection of objects that are grouped with an O
in one or more of the concept lattice), divided by the
total of all objects.
• A5: the average number of O’s properties that are
used together with other objects, divided by the total
of all properties.
• A6: the number of occurrence of the object in the
topic map divided by the number of occurrence of
the object with the same type (topic or association).
After the statistics are calculated for each topic and
association, the object profile can be concluded. For N
object, O1, O2, … ON, each component Ai for profile
vector P is calculated as in the equation:
N
P. Ai = ∑ Oj. Ai * Oj. A6
(1)
j =1
(where Oj.Ai is the component Ai on object j.)
Objects that are most relevant (regular object), which
has many properties of many other objects will be
maintained. Regular Objects are more important by the
means of semantic compared with another objects.
The object which is regular is proved using the
following conditions:
O.A1 ≥ Profile.A1
O.A2 ≥ Profile.A2
Condition is improved by adding a standard deviation.
Calculation of standard deviation is:
N
∑ | O .A
j
Std .dev. A3 =
3
j =1
N
− P. A3 |
(2)
Regular conditions can be changed using a coefficient
C. Relation of the objects with regular coefficients C and
the standard deviation is defined as follows:
O.A1 + C x std.dev.A1 ≥ P.A1
O.A2 + C x std.dev.A2 ≥ P.A2
Characterization phase will produce a list of regular
items that are stable, where the topic map has been filtered
to eliminate non-regular objects (objects that are less
semantic). After this stage, there will be a new list of
objects that are used as an input to Galois classification
algorithm. Lattice then formed and the new statistics are
calculated on the new object to create the new profile, and
so forth until all items become regular.
2.3.3 Clustering
The next step after characterization is clustering.
Clustering is based on the concept of Galois conceptual
classification, which was developed using cluster tree.
Elections of the father of a concept based on the
following hierarchy criteria:
1. First, based on the distance of each father with the
lower bound of the lattice. Distance is related to the
amount of edge between the father and the lower bound of
the lattice.
2. If the distance of a father of a node with the lower
bound of the lattice is smaller than the other nodes, then
the node is selected. The closer the distance from the
lower bound of the lattice, the more semantic the concept
is.
3. If there are multiple nodes on the minimum distance
from the lower bound of the lattice, the amount of its
properties’ weight which is contained in their intention are
then compared. Node with the highest weight is selected.
4. If several fathers meet criteria-3, then choose ones
that minimize the total number of branches in the tree.
5. If the criteria-4 has not been fulfilled, then several
trees were built based on several possible fathers.
Some other criteria that are required can be counted
from a cluster tree, such as lattice initial concept that is
not selected for clustering process. In addition, level of the
navigation, the distance between objects, and the
similarity between objects can be analyzed. Depth of the
tree shows the number of tree-level navigation is provided
for the user. Cluster distribution at each level of separation
can also provide important information for the user. If a
cluster does not have a father, it means that it can not be
generalized. In addition, the cluster that does not have any
children means that its level is the most specific level.
The distance between two clusters is average or
maximum or minimum distance between two objects (one
object in each cluster). O1 and O2 given as two objects,
P1 is a collection of properties owned by O1, whereas P2
is a collection of properties owned by O2. INTER also
given as slices of P1 and P2, and the UNION as a
combination of P1 and P2. The similarity of object O1 and
O2 can be calculated as in the equation:
card ( INTER )
S (O1, O 2) =
∑ wi
i =1
card (UNION )
∑ w' j
whereas the distance O1 and O2 is defined as follow:
3
1
S (O1, O 2)
Table 2. Characterization results
Statistics
(A1... A6)
Other
information
Testing is done on an XML topic map. Table 1 shows
the results of the classification.
Section A
(Coefficient
C=1.12)
Object 0
A1=0.10563
A2=0.28571
A3=0.08761
A4=0.08571
A5=0.32
A6=0.0
…
#iter=5
%object left=20
#regular object = 10
Section B
(Coefficient
C=1.18)
Object 0
A1=0.10204
A2=0.32432
A3=0.08648
A4=0.08108
A5=0.32
A6=0.0
…
#iter=5
%object left=58
#regular object =27
Table 2 shows that in general, the statistics on the
value of section A is larger when compared with the value
of statistics on the section B. Section A and The number
of objects left in section B is more than the number of
objects left in section A, shows that the filtering level is
different. Greater value of the coefficient gives larger
restrictions for the regular object, consequently the less
the number of objects that eliminated.
The results of clustering process can be seen in table 3.
We also used two different coefficient values.
Table 3. Clustering results
Cluster
Analysis
(4)
TESTING
Result
#object=42
#properties=42
#object=34
#properties=34
In characterization phase we used two different values
of coefficients to filter the same topic map. Sample results
of the characterization are shown in table 2.
(3)
j =1
D(O1, O 2) = 100 −
Table 1. Classification results
Process
Object dan property
establishment
Galois connection
Other
information
Section A
(Coefficient C=1.12)
between Obj1 &
Obj2
similarity: 0.28571
distance: 96.5
…
#level=4
#cluster=10
Section B
(Coefficient C=1.18)
between Obj1 &
Obj2
similarity: 0.5
distance: 98.0
…
#level=4
#cluster=38
Table 3 shows that the smaller the value of coefficient
C the more objects are grouped into a cluster. The higher
the level of the cluster then the more specific
object/cluster, the lower the level of the cluster the objects
are more general.
4
CONCLUSION AND FUTURE WORK
In this research we implement a semantic web mining
on the topic map and then test it to an XML topic map.
XML topic map as one of the structure of semantic web
data is able to show the data of the web more structured
than before. Therefore using the XML topic map, mining
on the web will become easier. Conceptual classification
stage evaluate topic map and display it in the form of
objects and properties. In addition, establishment of the
object and properties must be object oriented. The Galois
connection indicates the generalization/specialization
relations of the topic map objects. The object which has
many properties is more specific than other object which
has a few properties. Characterization topic map filter the
data in topic map. Filtering is used to eliminate the data
that is not relevant enough. The number of data eliminated
depends on the value of coefficient (C), the greater the
value of the coefficient, then the less the number of the
data that are eliminated. Clustering topic map shows the
topic map data in the different levels, indicating the
generalization/specialization data cluster.
Based on our testing results, we recommended the
following for further development: 1) Use several XML
topic map to ensure the results of our mining process 2)
Form more detail cluster representations, show that some
cluster are more relevant than others, and display more
detailed information of the cluster 3) develop semantic
web mining using another semantic structure, such as
XML and RDF.
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