a constellation graph based approach for ontology construction
TRANSCRIPT
A Constellation Graph based Approach for Ontology Construction
Yili Liu 1, a, Yang Yang (Corresponding Author)1,b 1Dept. of Management Science and Engineering, Tongji University, No. 1239 Siping Road, Shanghai,
China
Keywords: ontology; constellation graph; classes hierarchy.
Abstract. The ontology construction methodology frameworks used so far are limited in certain
domains lack of mature knowledge hierarchy and require the reference alignments to be specified
manually. This paper presents a constellation graph based method to build ontologies including two
critical steps: transform the property of the concepts abstracted into the corresponding data; draw a
constellation graph based on the data and the classes in the same constellation part constitute a new
kind of classes. This approach can facilitate ontology construction process with little human efforts
and be more time-saving. A practical example is used to illustrate the performance of this approach.
Introduction
Artificial Intelligence researchers have made great achievements in problem solving since
approximately 1970s [1]. Expert system is one of the achievements of problem-solving research [2].
Originally expert system aimed at a specific field to conduct knowledge solutions [3]. Nowadays
more and more solutions need intersections of different disciplines. Knowledge in a particular field
needs to be shared by other fields. Therefore, recent research focus on the complex processing of
common knowledge in multi-fields, including knowledge repository [4], large-scale model sharing
[5], system integration [6], knowledge representation and knowledge reuse [8]. As a valuable tool,
ontology was introduced to artificial intelligence domain and was gradually used in various academic
fields [9].
Ontology was originally a philosophical concept describing the nature of things. In artificial
intelligence field it can be used for conceptualizing knowledge in a field and can be reused by other
fields as a sharable granular object. To realize the two functions, methodologies are considered for
ontology construction, one of which is ontology construction methodology framework [10]. This
method makes the construction process relatively simple and clear in mind. However, this method
may spend much time sometimes, especially when the field contains a large quantity of concepts and
knowledge. This paper will make improvements on the existing methods using constellation graph
which will simplify the construction process with less manual intervention.
This paper is comprised of five sections. Section 1 introduces the background of this paper.
Section 2 reviews the existing ontology construction framework. Section 3 focuses on the application
of constellation graph in ontology construction. Section 4 presents a practical example to show how to
use this method. Section 5 concludes this paper.
Process of Ontology Construction
Definition of Ontology. The research about ontology was originally a branch of philosophy. In this
area ontology refers to physical objects, namely the explanation or description of an objective system.
Nowadays, ontology has been widely used as a term in many academic areas. Commonly accepted
statement of this concept is: “ontology is a formal specification of a shared conceptual model [11].”
Ontology is regarded as a set of shared terminology with public understanding (a common
vocabulary) that support researchers share the necessary information in a certain domain.
Applied Mechanics and Materials Vols. 397-400 (2013) pp 2540-2545Online available since 2013/Sep/03 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.397-400.2540
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Ontology Construction Process. Commonly ontology construction follows five steps including:
(1) Determining domain and scope of ontologies: Establish ontologies for specific research areas.
The greater the areas are, the greater the ontologies are. In most cases it is necessary to limit the
research scope.
(2) Reusing existing ontologies: If research in certain areas needs knowledge in other areas, reuse
of existing ontology directly can improve the utilization of resources.
(3) Listing the important terms in ontologies: Terms should be used to represent every physical
object and their attributes, relationships in the research fields.
(4) Defining classes and class hierarchy: Three different methods are used for class hierarchy:
top-down, bottom-up, and their combination. This step is critical in construction process.
(5) Defining attributes of defined class: When classes are defined, try to define their attributes.
Formalization of Ontology. Ontology can be described formally and definitely as following [12]:
(1) Describing the notions in the research field which are defined as classes denoted by iC
),,2,1( ni �= ;
(2) Describing different attributes of every class which are called slots denoted by k
ia
),,2,1( mk �= , },,2,1{ ni �∈ .
(3) Describing limitations of slots which are called facet denoted by k
is , ),,2,1( mk �= ,
},,2,1{ ni �∈ .
Thus every class can be denoted by ),( k
i
k
ii saC , },,2,1{ ni �∈ .
Previous construction of class hierarchy just merges classes in accordance with the subjective
understanding of fields. Besides, this kind of methods cannot offer a visualization of the hierarchy.
For solve this problem, constellation graph can be introduced to classify and merge related classes.
Ontology Construction Using Constellation Graph
By this method the samples are drawn into a semi-circle with one star standing for one sample. The
same kind of samples can form a constellation which looks like constellation image in astronomy,
which leads to this method’s name - constellation graph [13]. Since the stars are relatively
concentrated in a constellation, every constellation can be regarded as a class.
Transformation of Attributes to Data Matrix. The objects in a certain field can be considered as
the samples. Initially each of them can be defined as an independent class with its attributes. Some
attributes can be described by figures, which are called quantified attributes， while some of them can
be expressed by words, which is called qualitative attributes. Then all the attributes should be
translated into a data matrix. The quantified attributes expressed can be immediately introduced to the
matrix, while the qualitative attributes need be mapped to specific data in accordance following a
certain one-to-one mapping criteria so that they can be numeric coded and calculated. The mapping
process can be formulized as:
BA →ϕ
ϕ denotes a mapping function and A is the aggregate of qualitative attributes. B is an aggregate
containing a series of natural number. Following a practical standard, qualitative descriptions for
qualitative attributes can be mapped to corresponding natural numbers, one-to-one or many-to-one.
Thus, all the attributes can be mapped into a data matrix shown as Table 1.
Applied Mechanics and Materials Vols. 397-400 2541
Table 1: Data Matrix of a sample
( BAij ∈ )
Construction of Constellation Graph. Firstly, let the value of data { ijx } be translated into a data
{δ ij
} whose value lies into [0，π ] by the linear variation (Eq. 1):
πδj
jij
ijR
xx min−=
(1)
where ijni
j xx≤≤
=1
min min , ijni
j xx≤≤
=1
max max , jjj xxR minmax −= .
By this range standardization, the previous data matrix can be translated into another equal data
matrix [14].
Secondly, assign value to weight { jω } where jω ≥0，(j=1,2,…,p) and 11
=∑=
p
j
jω . jω can be
given a value, that means pp
121 ==== ωωω …… . jω can be also assigned differently
corresponding to the importance with practical experiences. Then the samples can get their point
coordinates following Eq.2:
∑ ∑
= =
l
j
l
j
ijiiji
1 1
sin,cos δωδω , l=1,2……,p; i=1，2……,n （2）
With the coordinates a constellation graph can be drawn.
According to visual closeness some samples in the same constellation can constitute a new class.
The attributes of the new class can be determined based on the original attribute. If classes cannot be
clearly visualized, change corresponding weights and repeat the above calculation till all samples can
be clearly classified.
Method Application with a Specific Example
Given that there are some brands of Chinese alcoholic drink. Firstly, every brand can be considered a
sample and an independent class. Every class has j attributes ( x j means the j
th attribute) illustrated in
Table 2.
Serial Number 1A sA ┅┅ nA
1 11A 12A ┅┅ nA1
2 21A 22A ┅┅ nA2
┇ ┇ ┇ ┇ ┇
m 1mA 2mA ┅┅ mnA
2542 Advanced Design and Manufacturing Technology III
Table 2 Attributes of Wines
Attributes
Wines
Alcohol
Degree
Color Taste
JianNanChun 38 Colorless Spicy
Qingdao Beer 5 Light Brown Harsh
MaoTai 45 Colorless Spicy
ZhangYu 10 Red Sweet
DongAWang 28 Colorless Spicy
The qualitative attributes can be translated into specific data:
A= {colorless, light brown, red} C= {spicy, harsh, sweet}
B= { 1 , 2, 3 } D= { 1, 2, 3 }
Table 2 can be transformed into a data matrix shown as Table 3 where xij means the number of j
variables of sample i.
Table 3 Data Matrix of attributes of wines
NO x1 x2
x3
1 38 1 1
2 5 2 2
3 45 1 1
4 10 3 3
5 28 1 1
Convert the above data matrix into matrix of δ ij shown in Table 4 using linear variation Eq. 1.
Table 4 Matrix of δ ij
δ ij 1 2 3
1 0．825π 0 π
2 0 0.5π 0.5π
3 π 0 π
4 0．125π π 0
5 0．575π 0 π
In this scenario p = 3, n = 5. According to the importance of enjoyment the attributes weight
differently. Let 5.01 =ω , 2.02 =ω , 3.03 =ω . Then the coordinates of five samples can be figured
out: 1.(-0.5995,0.0226), 2.(0.5,0.5), 3.(-0.6,0) 4.(0.5995, 0.0034) , 5.(-0.5995, 0.0158).
Applied Mechanics and Materials Vols. 397-400 2543
A constellation graph can be drawn as Figure 1:
Figure 1 Constellation Graph of the five kinds of wine
As is shown in Figure 1, samples 1, 3, 5 visually belong to the same part of the graph and can be
classified as one class while Samples 2, 4 can constitute another class. In this way, samples can be
explicitly classified as classes and make up a class hierarchy.
Then an ontology structure shown in Figure 2 can be obtained.
Figure 2 Hierarchical Structure of wine Ontology
Conclusion
The construction of the class hierarchy is one of the important steps in the ontology development
process. This paper proposes a method based on the constellation graph to construct class hierarchy.
Properties of the concept can be transformed into corresponding data. Then the data matrix can be
figured out to generate coordinates of the samples in a constellation graph. In the drawn graph the
samples in the same constellation can be classified as a new class. In practice, programs can be created
to automatically extract domain ontology. This will greatly improve the productivity of ontology
construction.
Acknowledgements
This work was financially supported by the Chinese National Science Foundation of China Grant
71101110, 71202034.
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2544 Advanced Design and Manufacturing Technology III
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