A context-aware semantic similarity model for ontology

Abstract

While many researchers have contributed to the field of semantic similarity models so far, we find that most of the models are designed for the semantic network environment. When applying the semantic similarity model within the semantic-rich ontology environment, two issues are observed: (1) most of the models ignore the context of ontology concepts and (2) most of the models ignore the context of relations. Therefore, in this paper, we present a solution for the two issues, including a novel ontology conversion process and a context-aware semantic similarity model, by considering the factors of both the context of concepts and relations, and the ontology structure. Furthermore, in order to evaluate this model, we compare its performance with that of several existing models' performance in a large-scale knowledge base, and the evaluation result preliminarily proves the technical advantage of our model in ontology environments. Conclusions and future works are described in the final section. Copyright © 2010 John Wiley & Sons, Ltd.

Full text

A Context-Aware Semantic Similarity Model for
Ontology Environments1
Hai Dong, Farookh Khadeer Hussain, Elizabeth Chang
Digital Ecosystems and Business Intelligence Institute,
Curtin University of Technology, Perth WA 6845, Australia
SUMMARY
Whilst many researchers have contributed to the field of semantic similarity models so far, we find most of the models
are designed for the semantic network environment. When applying the semantic similarity model within the semantic-
rich ontology environment, two issues are observed: 1) most of the models ignore the context of ontology concepts; 2)
most of the models ignore the context of relations. Therefore, in this paper, we present a solution for the two issues,
including a novel ontology conversion process and a context-aware semantic similarity model, by considering the
factors of both the context of concepts and relations, and the ontology structure. Furthermore, in order to evaluate this
model, we compare its performance with several existing models’ performance in a large scale knowledge base, and the
evaluation result preliminarily proves the technical advantage of our model in ontology environments. Conclusions and
future works are described in the final section.
Received:
KEYWORDS: ontology, OWL, semantic network, semantic similarity model.
1. INTRODUCTION
Semantic relatedness refers to human judgment about the extent to which a given pair of concepts are
related to each other [3]. Studies have shown that most people agree on the relative semantic relatedness of
most pairs of concepts [5, 6]. Therefore, many technologies have been developed to date in order to
precisely measure the extent of similarity relatedness and similarity between concepts in multiple
disciplines, such as information retrieval (IR) [1, 8-12], natural language processing (NLP) [7, 13-15],
linguistics [17], health informatics [19], bioinformatics [3, 20-23], web services [25], ontology
extraction/matching [45-47] and other fields. In the fields of IR and NLP, the researches primarily focus on
word sense disambiguation [7, 12], multimodal document retrieval [26], text segmentation [10, 14] and
query preciseness enhancement [8, 9]. In the linguistic area, the researches emphasize computing semantic
similarity between uncertain or imprecise concept labels [17]. In the health domain, the researchers are
mainly concerned with seeking similar health science terms. In the field of bioinformatics, the focus is on
measuring the similarity between concepts from the gene ontology [20-23]. In the field of web services, the
researches concentrate on semantic service discovery [25]. In the field of ontology extraction/matching,
semantic similarity models are used in the process of ontology similarity measurement [45-47]. Moreover,
the semantic similarity models also can be used to estimate the similarity between land use and land cover
classification systems [27].
However, when exploring those semantic similarity models, we observe that most of the existing models
focus only on the semantic network environment but ignore the special features of the ontology
environment. For example, most of the models do not have specific solutions to process the context of
concept attributes and the context of relations when estimating similarity between concepts. Based on this
finding, we develop a novel context-aware solution for the semantic similarity measure in the ontology
environment. This solution contains an ontology conversion process and a hybrid semantic similarity model,
which involves assessing the concept similarity from the perspectives of both the ontology structure and the
context of ontology concepts and relations.
1 This is a preprint version of the paper: Dong, H., Hussain, F.K., Chang, E.: A context-aware semantic
similarity model for ontology environments. Concurrency and Computation: Practice and Experience 23(2)
(April 2011) pp. 505-524. Download link: http://onlinelibrary.wiley.com/doi/10.1002/cpe.1652/abstract

The remainder of the paper is organized as follows. In Section 2 we conduct a detailed comparison
between ontology and the semantic network, and then review and analyse the existing semantic similarity
models in order to discover the issues that arise when applying the models within the ontology environment.
In Section 3, we provide an ontology conversion process to preliminarily address the issues found in
Section 2. In Section 4, we present the proposed hybrid semantic similarity model. In Section 5, to
thoroughly validate the model, we implement a series of experiments and perform scientific evaluations
and experimentations. The conclusion is drawn and future work is proposed in the final section.
2. RELATED WORKS
2.1 Ontology and semantic network
In the field of information science, ontology is defined by Gruber [28] as “an explicit specification of
conceptualization”. An ontology primarily consists of the following components:
 Classes that define a group of individuals that share the same features.
 Properties that describe relations between classes. In OWL, there are two sorts of properties as
follows:
o ObjectProperty that defines relations between two or more than two classes, and
o DatatypeProperty that defines relations between instances of classes and RDF literals and
XML schema datatypes [29].
 Restrictions and characteristics that describe constraints on relations. In OWL, restrictions include
allValuesFrom (

), someValuesFrom (

), hasValue (

), cardinality (

), minCardinality ( ),
maxCardinality ( ); characteristics include FunctionalProperty (one property has a unique value),
InverseOf (one property is the inverse of another property), InverseFunctionalProperty (the inverse
of one property is functional), TransitiveProperty (properties are transitive), and SymmetricProperty
(properties are symmetric) [29].
 Axioms that describe the rules followed by an ontology when applying it to a domain. In OWL, the
class axioms include one of (enumerated classes) , disjointWith (classes are disjointed with each
other), equivalentClass (two classes are equivalent) , subClassOf (one class is specification of
another class) [29].
A semantic network is defined as “a graphic notation for representing knowledge in patterns of
interconnected nodes and arcs” [30]. WordNet is a typical example of a semantic network, in which words
or phrases are represented as nodes and are linked by multiple relations. The most common relations are
meronymy (A is a part of B), holonymy (B is part of A), hyponymy (A is a subordinate of B), hypernymy (A
is superordinate of B), synonymy (A is a synonym of B), and antonymy (A is an opposite of B).
In Table 1, we make a general comparison between ontologies and semantic networks based on their
components. The main differences are that ontology concepts and relations can be defined with more
attributes, restrictions and characteristics, compared with single-word/phrase-composed counterparts in
semantic networks. Therefore, it can be concluded that ontologies can express more semantic information
than can semantic networks.
Table 1. Comparison between ontologies and semantic networks
2.2 Semantic similarity models
In the literature there are many similarity measures. For the purpose of discussion, we divide them into
three main categories according to the utilized information as follows – edge (distance)-based models [1, 2,
4, 9, 12, 31, 32], node (information content)-based models [7, 16, 18] and hybrid models [13, 24, 33, 34].
Components Ontologies Semantic Networks
Classes Have individuals. Do not have individuals.
Properties Have object properties and
datatype properties.
Do not have datatype properties.
Restrictions and Characteristics Have restrictions and
characteristics.
Do not have restrictions and
characteristics.
Axioms Have axioms. Do not have one of and
disjointWith.

In the rest of the section, we will briefly introduce the three categories and the typical models in each
category, and analyze their limitations when applying them within the ontology environment.
Edge (Distance)-based Models. Edge-based models are based on the shortest path between two nodes
in a definitional network. Definitional networks are a type of hierarchical/taxonomic semantic network, in
which all nodes are linked by is-a relations [30]. The models are based on the assumption that all nodes are
evenly distributed and are of similar densities and the distance between any two nodes is equal. They can
also be applied to a network structure.
One typical edge-based model was provided by Rada [1], and is described as:
For two nodes C1 and C2 in a semantic network,
12 1 2
Distance ( , ) = Minimum number of edges seperating and CC C C
(1)
and the similarity between C1 and C2 is given by
12 12
( , ) 2 Distance( , )
Rada
s
im C C Max C C  (2)
where Max is the maximum depth of a definitional network.
In order to ensure the interval of simRada is between 0 and 1, Equation 2 can also be expressed as
12
12
Distance( , )
(, )1 2
Rada
CC
sim C C Max
  (3)
Leacock et al. [2] considered that the number of edges on the shortest path between two nodes should be
normalized by the depth of a taxonomic structure, which is expressed mathematically as
12
12
Minimum number of edges separating and
Distance ( , ) = 2
CC
CC
M
ax (4)
and the similarity between C1 and C2 is given by
12 12
( , ) = - log(Distance ( , ))
Leacock
s
im CC CC (5)
Wu and Palmer[4] mentioned the node that subsumes two nodes when computing the similarity between
the two nodes, which can be expressed mathematically as follows:
3
&12
12 3
2
(, ) 2
Wu Palmer
N
sim C C NN N

 (6)
where C3 is the most informative node that subsumes C1 and C2, N1 is the minimum number of edges
from C1 to C3, N2 is the minimum number of edges from C2 to C3, N3 is the depth of C3.
Node (Information Content)-based Models. Information content-based models are used to judge the
semantic similarity between concepts in a definitional network or in a corpus, based on measuring the
similarity by taking into account information content, namely the term occurrence in corpora or the
subsumed nodes in taxonomies. These models can avoid the disadvantage of the edge counting approaches
which cannot control variable distances in a dense definitional network [7].
Resnik [7] developed such a model whereby the information shared by two concepts can be indicated by
the concept which subsumes the two concepts in a taxonomy. Then, the similarity between the two
concepts C1 and C2 can be mathematically expressed as follows:
12
Resnik 1 2 ( , )
( , ) max [ log(P( ))]
CSCC
s
im C C C


(7)

where S(C1, C2) is the set of concepts that subsume both C1 and C2, and P(C) is the possibility of
encountering an instance of concept C.
Lin [16]’s semantic similarity model is the extension of Resnik’s model, which measures the similarity
between two nodes as the ratio between the amount of commonly shared information of the two nodes and
the amount of information of the two nodes, which can be mathematically expressed as follows:
Re 1 2
12
2(,)
() ()
snilk
Lin
s
im C C
sim IC C IC C

 (8)
Pirro [18] proposed a feature-based similarity model, which is based on Tversky’s theory that the
similarity between two concepts is the function of common features between the two concepts minus those
in each concept but not in another concept [35]. By integrating Resnik’s model, the similarity model can be
mathematically expressed as follows:
Re 1 2 1 2 1 2
&12
12
3(,)()()
(, ) 1
snik
PS
s
im C C IC C IC C if C C
sim C C if C C



 (9)
Hybrid Models. Hybrid models are comprised of multiple factors for similarity measure. Jiang and
Conath [24] developed a hybrid model that uses the node-based theory to enhance the edge-based model.
Their method takes into account the factors of local density, node depth and link types. The weight between
a child concept C and its parent concept P can be measured as:
()1
(,) ( (1 ) )( )( () ())(,)
() ()
EdP
wtCP ICC ICP TCP
EP dP



  (10)
where d(P) is the depth of node P, E(P) is the number of edges in the child links, Eis the average
density of the whole hierarchy, T(C, P) represents the link type, and α and β (α ≥ 0, 0 ≤ β ≤ 1) are the
control parameters of the effect of node density and node depth on the weight.
The distance between two concepts is defined as follows:
12 12
12
{(,)(,)}
Distance( , ) = ( , ( ))
C path C C LS C C
CC wtCpC

 (11)
where path(C1, C2) is the set that contains all the nodes in the shortest path from C1 to C2, and LS(C1, C2)
is the most informative concept that subsume both C1 and C2.
In some special cases such as when only the link type is considered as the factor of weight computing
(α=0, β=1, and T(C, P) =1), the distance algorithm can be simplified as follows:
12 1 2 Re 12
Distance( , ) ( ) ( ) 2 ( , )
snik
CC ICC ICC sim CC (12)
where IC(C)=-logP(C).
Finally, the similarity value between two concepts C1 and C2 is measured by converting the semantic
distance as follows:
&12 12
( , ) = 1 Distance( , )
Jiang Conath
s
im CC CC (13)
In addition, Seco [36]’s research showed that the similarity equation can also be expressed as
12
&12
Distance( , )
(, ) = 1 2
Jiang Conath
CC
sim C C  (14)

The testing results show that the parameters α and β do not heavily influence the similarity computation
[24].
Li et al. [13] proposed a hybrid semantic similarity model combining structural semantic information in
a nonlinear model. The factors of path length, depth and density are considered in the assessment, which
can be mathematically expressed as
12
12
12
(, )
1
hh
l
hh
Li
ee
eifCC
sim C C ee
if C C













(15)
where l is the shortest path length between C1 and C2, h is the depth of the subsumer of C1 and C2, α and
β are the effect of l and h on the similarity measure.
In order to analyze the features of these models described above, in Table 2, we present a horizontal
comparison for these semantic similarity models. By means of combining this comparison and the
comparison between ontologies and semantic networks displayed in Table 1, we conclude that there are
two limitations when applying these models in an ontology environment, which can be expressed as
follows:
First, the edge-based and node-based models primarily focus on estimating similarity for nodes in
definitional networks. Since types of relations are one-fold in definitional networks, the factor of types of
relations and contexts of relations are ignored when calculating similarity. However, as introduced in
Section 2.1, in an ontology environment, the types of relations are various, and relations can be defined by
multiple restrictions. Obviously, the two factors cannot be ignored when computing similarity for ontology
concepts.
Second, these models all ignore the factor of the context of nodes when computing semantic similarity,
due to the feature of nodes in semantic networks, in which a node is composed of a single word or phrase
without adequate properties. In contrast, in the ontology environment, ontology concepts are defined with
sufficient datatype, and object type properties, and the combinations of these properties can be regarded as
the crucial identifications for the concepts. Obviously, the contexts of ontology concepts cannot be ignored
when computing similarity between ontology concepts.
Consequently, in order to address the two limitations of these semantic similarity models, in the rest of
this paper, we present an ontology conversion process and a context-aware semantic similarity model for an
ontology environment.
Table 2. Comparison of the typical semantic similarity models
3. ONTOLOGY CONVERSION PROCESS
Category Models Working Environment Measure Factors
Edge-based Rada [1] Definitional networks Shortest path
Leacock et al. [2] Definitional networks Shortest path
Wu and Palmer[4] Definitional networks Shortest path and node
depth
Node-based Resnik [7] Definitional networks or corpora Subsumed nodes in
definitional networks or
word occurrences in corpora
Lin [16] Definitional networks or corpora Subsumed nodes in
definitional networks or
word occurrences in corpora
Pirro [18] Definitional networks or corpora Subsumed nodes in
definitional networks or
word occurrences in corpora
Hybrid Jiang and Conath [24] Semantic networks Shortest path, subsumer,
local density, node depth
and link types
Li et al. [13] Semantic networks Shortest path, node depth
and local densit
y

3.1 Lightweight ontology space
In order to address the limitations of the semantic similarity models, we provide a concept of lightweight
ontology space, which includes two basic definitions as follows:
Definition 1. Pseudo-concept
We define a pseudo-concept ς for an ontology concept C, which can be represented as a tuple as follows:


,, , , , ,
ij j
j
xy
ij
CC


  



 (16)
where in OWL-annotated semantic web documents, C is the name (or Uniform Resource Identifier
(URI)) of the concept C, each [] is a property tuple including a property and its restriction (if available), δi
(i = 1…n) is a datatype property(s) of the concept C, γδi is a restriction (s) for the datatype property δi, οj (j
= 1…m) is an object property(s) of the concept C, γοj is a restriction(s) for the object property οj, Cοj
x (x =
1…k) is a concept(s) related by the object property οj, and λοj
y (y = 1…k-1) is a Boolean operation(s)
between concepts Cοj
x.
The aim of defining the pseudo-concept is to encapsulate all properties, and restrictions and
characteristics of the properties of a concept into a corpus for the concept, which enables the feasibility of
assessing similarity between concepts based on the contexts of their pseudo-concepts.
Definition 2. Lightweight ontology space
Based on the definition of pseudo-concept, we define a lightweight ontology space as a space of pseudo-
concepts, in which pseudo-concepts are linked only by is-a relations [37]. An is-a relation is a
generalization/specification relationship between an upper generic pseudo-concept and a lower specific
pseudo-concept. In OWL documents, the is-a relation is represented by subClassOf. The aim of
constructing a pseudo-concept space is to simplify the complicated ontology structure and hence to
construct a definitional network-like taxonomy. This taxonomy enables the feasibility of measuring concept
similarity based on the existing semantic similarity models.
3.2 Theorems for ontology conversion process
In order to convert an ontology to a lightweight ontology space, we need a conversion process. It needs to
be noted that the proposed ontology conversion process takes place only in OWL Lite or OWL DL-
annotated semantic web documents. Additionally, from the definitions above, it can be observed that the
conversion process concerns only the schema (concept) level but not the instance level, because the
information of instances is special to some degree and cannot completely represent belonged concepts. In
order to consider the complexity and flexibility in defining restrictions and characteristics for object
properties and datatype properties, a set of theorems, aligned with the conversion process, needs to be
defined. The theorems can be divided into six categories in accordance with the components of a pseudo-
concept, which are the theorems regarding the conversion of concepts, datatype properties, object
properties, property restrictions, property characteristics and Boolean operations. In the rest of this section,
we introduce and illustrate these theorems based on the six divisions.
Theorem 1. If C is the name (URI) of a concept, then C is a component of its pseudo-concept.
For example, for the concept C1 shown in Fig. 1, its pseudo-concept ς1 = {C1}
Fig. 1. Example of an ontology concept
Theorem 2.1. If C is the name (URI) of a concept, and δ is a datatype property of C, then δ is a
component of its pseudo-concept.

For example, for the concept C1 shown in Fig. 2, it has a datatype property δ. According to Theorem 2.1,
its pseudo-concept ς1 = {C1, δ}.
Fig.2. Example of an ontology concept with a datatype property
Theorem 2.2. If C1 is the name (URI) of a concept, δ is a datatype property of C1, and C2 is the name
(URI) of a subclass of C1, then δ is a component of the pseudo-concept of C2.
For example, for the concepts C1 and C2 shown in Fig. 3, C1 has a datatype property δ, and C2 is a
subclass of C1. According to Theorem 2.2, the pseudo-concept ς2 for C2 is a tuple that can be expressed as
{C2, δ}
Fig.3. Example of an inherited ontology concept with a datatype property
Theorem 3.1. If C1 is the name (URI) of a concept, ο is an object property of C1, and C2 is the name
(URI) of a concept that relates to C1 through ο, then ο and C2 are the components of the pseudo-concept of
C1.
For example, for the concepts C1 and C2 shown in Fig. 4, C1 has an object property ο which connects C1
to C2. According to Theorem 3.1, the pseudo-concept ς1 for C1 is a tuple that can be expressed as {C1, ο,
C2}.
C1 C2
ο
Fig. 4. Example of an ontology concept with an object property
Theorem 3.2. If C1 is the name (URI) of a concept, ο is an object property of C1, C2 is the name (URI)
of a concept that relates to C1 through ο, and C3 is the name (URI) of a subclass of C1, then ο and C2 are the
components of the pseudo-concept of C3.
For example, for the concepts C1, C2 and C3 shown in Fig. 5, C1 has an object property ο which connects
C1 to C2, and C3 is a subclass of C1. According to Theorem 3.2, the pseudo-concept ς3 for C3 is a tuple that
can be expressed as {C3, ο, C2}

C1 C2
ο
C3
Fig .5. Example of an inherited ontology concept with an object property
Theorem 4.1. If C is the name (URI) of a concept, δ is a datatype property of C, and γ is a restriction for
δ, then the tuple [δ, γ] is a component of the pseudo-concept of C.
For example, for the concept C1 shown in Fig. 6, it has a datatype property δ, which has a value
restriction hasValue and a cardinality restriction minCardinality 5. According to Theorem 4.1, its pseudo-
concept ς1 = {C1, [δ, hasValue minCardinality 5]}.
Fig. 6. Example of an ontology concept with a restricted datatype property
Theorem 4.2. If C1 is the name (URI) of a concept, ο is an object property of C1, C2 is the name (URI)
of a concept that relates to C1 through ο, and γ is a restriction for the datatype property ο, then the tuple [ο, γ]
is a component of the pseudo-concept of C1.
For example, for the concepts C1 and C2 shown in Fig. 7, C1 has an object property ο which connects C1
to C2, and ο has a property restriction someValuesFrom and a cardinality restriction cardinality 1.
According to Theorem 3.2, the pseudo-concept ς1 for C1 is a tuple that can be expressed as {C1, [ο,
someValuesFrom], C2, [ο, cardinality 1], C2}.
C1 C2
-someValuesFrom : C2
-cardinality 1 : C2
ο
Fig. 7. Example of an ontology concept with a restricted object property
Theorem 5.1. If C is the name (URI) of a concept, and δ is a functional datatype property of C, then the
tuple [δ, cardinality 1] is a component of the pseudo-concept of C.
For example, concept C1 shown in Fig. 8 has a functional datatype property δ. According to Theorem
2.1, its pseudo-concept ς1 = {C1, [δ, cardinality 1]}.

Fig. 8. Example of an ontology concept with a functional datatype property
Theorem 5.2. If C1 is the name (URI) of a concept, ο is a functional object property of C1, and C2 is the
name (URI) of a concept that relates to C1 through ο, then the tuple [ο, cardinality 1] is the component of
the pseudo-concept of C1.
For example, for the concepts C1 and C2 shown in Fig. 9, C1 has a functional object property ο which
connects C1 to C2. According to Theorem 5.2, the pseudo-concept ς1 for C1 is a tuple that can be expressed
as {C1, [ο, cardinality 1], C2}.
C1 C2
FunctionalProperty ο
Fig. 9. Example of an ontology concept with a functional object property
Theorem 5.3. If C1 is the name (URI) of a concept, ο is a transitive object property of C1, C2 is the name
(URI) of a concept that relates to C1 through ο, and C3 is the name (URI) of a concept that relates to C2
through ο, then ο, C2 and C3 are the components of the pseudo-concept of C1.
For example, for the concepts C1, C2 and C
3 shown in Fig. 10, C1 has a transitive object property ο
which connects C1 to C2, and C2 has ο which connects C2 to C3. According to Theorem 5.3, the pseudo-
concept ς1 for C1 is a tuple that can be expressed as {C1, ο, C2, ο, C3}.
Fig.10. Example of ontology concepts with a transitive object property
Theorem 5.4. If C1 is the name (URI) of a concept, ο is a symmetric object property of C1, and C2 is the
name (URI) of a concept that relates to C1 through ο, then ο and C2 are the components of the pseudo-
concept of C1, and ο and C1 are the components of the pseudo-concept of C2.
For example, for the concepts C1 and C2 shown in Fig. 11, C1 has a symmetric object property ο which
connects C1 to C2. According to Theorem 5.4, the pseudo-concept ς1 for C1 is a tuple that can be expressed
as {C1, ο, C2}, and the pseudo-concept ς2 for C2 is a tuple that can be expressed as {C2, ο, C1}.
C1 C2
SymmetricProperty ο
Fig.11. Example of ontology concepts with a symmetric object property

Theorem 5.5. If C1 is the name (URI) of a concept, ο1 is an inverse functional object property of C1, C2
is the name (URI) of a concept that relates to C1 through ο1, and ο2 is the inverse property of ο1, then the
tuple [ο2, cardinality 1] is the component of the pseudo-concept of C2.
For example, for the concepts C1 and C2 shown in Fig. 12, C1 has a inverse functional object property ο1
which connects C1 to C2, and ο2 is the inverse property of ο1.According to Theorem 5.5, the pseudo-concept
ς2 for C2 is a tuple that can be expressed as {C2, [ο2, cardinality 1], C1}.
C1 C2
InverseFunctionalProperty ο1
-inverseOf ο1
ο2
Fig.12. Example of ontology concepts with an inverse functional object property
Theorem 6.1. If C1 is the name (URI) of a concept, ο is an object property of C
1, C2 and C3 are the
names (URI) of concepts that relate to C1 through ο, and λ is a Boolean operation (unionOf or
intersectionOf) between C2 and C3 for ο, then ο, C2, λ and C3 are the components of the pseudo-concept of
C1.
For example, for the concepts C1, C2 and C3 shown in Fig. 13, C1 has an object property ο which
connects C1 to C2 and C3, and C2 and C3 are connected with intersectionOf. According to Theorem 6.1, the
pseudo-concept ς1 for C1 is a tuple that can be expressed as {C1, ο, C2, intersectionOf, C3}.
Fig .13. Example of ontology concepts connected with a Boolean operation (unionOf or intersectionOf)
Theorem 6.2. If C1 is the name (URI) of a concept, ο is an object property of C1, and C2 is the name
(URI) of a concept that relates to C1 through the complement of ο, then complementOfC2 is a component of
the pseudo-concept of C1.
For example, for the concepts C1 and C2 shown in Fig. 14, C1 has an object property ο which connects
C1 to the complement of C2. According to Theorem 6.2, the pseudo-concept ς1 for C1 is a tuple that can be
expressed as {C1, ο, complementOfC2}.

C1 C2
o
-complementOf
Fig .14. Example of ontology concepts connected with a complementOf operation
4. CONTEXT-AWARE SEMANTIC SIMIALIRITY MODEL
As described in the previous section, there are two advantages for the ontology conversion process as
follows:
 Each ontology concept is converted to a pseudo-concept, which is a tuple of plain texts. Since the
pseudo-concepts include almost all the features of ontology concepts, it is possible to measure the
similarity between concepts based on the contexts of pseudo-concepts.
 An ontology with a complicated structure can be simplified to a lightweight ontology by means of
the conversion process. The taxonomic lightweight ontology enables the adoption of the existing
semantic similarity models to measure the similarity between concepts.
In this section, we propose a hybrid semantic similarity model, by assessing the concept similarity from
the two perspectives above. This model integrates a pseudo-concept-based semantic similarity model and a
lightweight ontology structure-based semantic similarity model, which are introduced respectively in
Section 5.1 and 5.2.
4.1 Pseudo-concept-based semantic similarity model
In the IR field, in order to measure the similarity between two corpora, a usual method is to use cosine
correlation, which can be mathematically expressed as follows:
cos (, ) || || || ||
xy
sim x y
x
y





(17)
where each corpus can be represented by a vector in which each dimension corresponds to a separate
term, and the weight of each term in the vector can be obtained by the TF-IDF scheme.
In this research, in order to measure the similarity between two pseudo-concepts, we adopt the cosine
correlation aligned with the pseudo-concept model displayed in Equation 16. There are some special
features in the pseudo-concept model, which can be described as follows:
 Each component is separated by a comma and is viewed as a basic unit for the measure. For
example, in the property tuple [ο, cardinality 1], cardinality 1 is seen as a whole for the
measure.
 The property tuples have the following features:
o Each property tuple contains no more than two items, which are a property and a
restriction (if necessary).
o The weights of the terms occurring in each property tuple should be averaged, as a
property tuple should be treated as same as other single items in a pseudo-concept
tuple in the measure. For example, in the tuple [ο, someValuesFrom], if the TF-IDF
weight of o is 0.56 and it of someValuesFrom is 0.44, then their actual weights should
be 0.28 and 0.22, as the average weight of the tuple is 0.5.
o In each tuple, a property has a priority over its affiliated restriction in the measure,
since the restriction is a modifier of the property. In other words, if there are two
property tuples, their properties are different and their restrictions are same, then there
is no similarity between the two property tuples. For example, a pseudo-concept ς1 has
a tuple [ο1, someValuesFrom] and another pseudo-concept ς2 has a tuple [ο2,
someValuesFrom], the similarity value between the two tuples is 0 as 12
oo.

In accordance with the features of the pseudo-concept model, we design an enhanced cosine correlation
model to implement the similarity measure, which is displayed in Fig. 15.
Fig. 15. Pseudo-code of the pseudo-concept-based semantic similarity model
4.2 Lightweight ontology structure-based semantic similarity model
Input: A list of pseudo-concepts ς = (ς1, ς2…ςm).
Output: A matrix P where each element Pij is the similarity value between pseudo-concept ςi and ςj.
Algorithm
for i = 1 to m
Read ςi;
Generate an array of index term T = (t1, t2…tn);
Put all the items in the tuples of ςi into an array Θi;
end for
for i = 1 to m
Set l to the number of items in Θi;
for k = 1 to l
for j = 1 to n
if Θi,k = tj then
Put j into an array Δi;
end if
end for
end for
end for
for i = 1 to m
for j = 1 to n
Set wij to the TF-IDF weight of tj in ςi;
Set l to the number of items in Θi;
for k = 1 to l
if j = Θi,k then
wij = 0.5×wij;
end if
end for
put wij into i

;
end for
Normalize i

 by | i

| = 1;
end for
for i = 1 to m
for j = 1 to m
for k = 1 to n
Set a to the number of items in Δi;
Set b to the number of items in Δj;
for u = 1 to a
for v = 1 to b
if k = Δi,u and u%2 = 0 then
if k = Δj,v and v%2 = 0 then
if ,1 ,1
,,
0
iu jv
ij
ww



then
wik×wjk = 0;
end if
end if
end if
end for
end for
Pij = Pij + wik×wjk;
end for
end for
end for

As mentioned previously, the lightweight ontology structure enables the use of existing semantic similarity
models in the ontology environment. Here we take the means of Resnik’s node-based model (Equation 7)
for the lightweight ontology-based semantic similarity measure. Nevertheless, one limitation of Resnik’s
model is that its interval is [0, ]. For the purpose of according with the interval of the cosine correlation,
we normalize Resnik’s model by given
12
(,)
12
Resnik 1 2
12
max [ log(P( ))]
max [ log(P( ))]
|(,)|
1
Sif
sim
if

















(18)
where Θ is the collection of concepts in a lightweight ontology.
4.3 Hybrid semantic similarity model
Here we leverage the two semantic similarity models above by means of a weighted arithmetic mean,
which can be expressed as
1 2 cos 1 2 Resnik 1 2
( , ) (1 ) (, ) | (, )|sim C C sim sim


  
   (19)
where 01

.
5. EVALUATION
5.1 Performance indicators
In order to empirically compare our proposed model with the existing models, we utilize the six most
widely used performance indicators from the IR field as the evaluation metrics. The performance indicators
in this experiment are defined as follows:
Precision. Precision in the IR field is used to measure the preciseness of a search system [38]. Precision
for a single concept refers to the proportion of matched and logically similar concept in all concepts
matched to this concept, which can be represented by Equation 20 below:
Number of matched and logically similar concepts
Precision(S) = Number of matched concepts (20)
With regard to the whole collection of concepts in an ontology, the total precision is the sum of the
precision value for each concept normalized by the number of concepts in the collection, which can be
represented by Equation 21 below:
1Precision(S )
Precision(T)=
n
i
i
n

 (21)
Mean average precision. Before we introduce the definition of mean average precision, the concept of
average precision should be defined. Average precision for a single concept is the average of precision
values after truncating a ranked concept list matched by this concept after each of the logically similar
concepts for this concept [38]. This indicator emphasizes the return of more logically similar concepts
earlier, which can be represented as:
Sum(Precision @ Each logically similar concept in a list)
Average precision(S) = Number of matched and logically similar concepts in a list
(22)

Mean average precision refers to the average of the average precision values for the collection of
concepts in an ontology, which can be represented as:
1Average precision(S )
Mean average precision =
n
i
i
n

 (23)
Recall. Recall in the IR field is used to measure the effectiveness of a search system [38]. Recall for a
single concept is the proportion of matched and logically similar concepts in all concepts that are logically
similar to this concept, which can be represented by Equation 24 below:
Number of matched and logically similar concepts
Recall(S)= Number of logically similar concepts (24)
With regard to the whole collection of concepts in an ontology, the total recall is the sum of the recall
value for each concept normalized by the number of concepts in the collection, which can be represented
by Equation 25 below:
1Recall(S )
Recall(T)=
n
i
i
n

 (25)
F-measure. F-measure in the IR field is used as an aggregated performance scale for a search system
[38]. In this experiment, F-measure is the mean of precision and recall, which can be represented below as:
2 Precision Recall
F-measure = Precision Recall

 (26)
When the F-measure value reaches the highest level, it means the aggregated value between precision
and recall reaches the highest level at the same time.
F-measureβ. F-measureβ is another measure that combines precision and recall, and the difference is that
users can specify the preference on recall or precision by configuring different weights [39]. In this
experiment, we employ F-measure (β=2) that weights recall twice as much as precision, which is close to
the fact that most search engines are concerned more with recall than precision, as a result of most users’
purposes in obtaining information [40]. F-measure (β=2) can be represented below as:
2
2
(1 ) Precision Recall 5 Precision Recall
F-measure ( =2)= = 4 Precision+Recall
Precision+Recall


   

 (27)
All of the above indicators have the same limitation – they do not consider the number of non-logically
similar concepts in a matched concept collection of a concept. Furthermore, if there is no logically similar
concept in the matched collection, recall cannot be defined. To resolve this issue, we need another
performance indicator – Fallout. In this experiment, fallout for a single concept is the proportion of a non-
logically similar concept matched by this concept in the whole collection of non-logically similar metadata
for this concept [38], which can be represented as:
Number of matched and non-logically similar concept
Fallout(S) =
Number of non-logically similar concept
(28)
With regard to the whole collection of concepts, the total fallout value is the sum of the fallout value for
each concept normalized by the number of concepts in an ontology, which can be represented as:

1Fallout(S )
Fallout(T)=
n
i
i
n

 (29)
In contrast to other performance indicators, the lower the fallout value, the better is the search
performance.
5.3 Experiments
In this experiment, we empirically evaluate the performance of the proposed model by comparing its
performance with the existing semantic similarity models, in terms of the performance indicators
introduced above. For the evaluation purpose we choose several typical semantic similarity models,
including Rada’s model (Equation 3) from the edge-based models, Resnik’s model (Equation 7) and Lin’s
model (Equation 8) from the node-based models and Jiang and Conath’s model (Equation 14) from the
hybrid models. In order to obtain precise data, we implement the subsequent experiments in a large scale
knowledge base – a health service ontology, which is a conceptualization and shared vocabulary of the
available health services. The ontology consists of more than 200 concepts and around 10000 instances,
and its details can be found from [41].
In the IR field, when a query is sent to a search system, a list of results with similarity values is returned
from the system. Then the search system needs to decide an optimal threshold value which is used to filter
the irrelevant results with lower similarity values, in order to obtain the best performance [42-44].
Analogously, in our subsequent experiments, as a result of that the performance of each model being
different on different threshold values, we need to find the best performance for each model. Hence, we
need to find the optimal threshold value for each model where each model can achieve the best
performance. Consequently, for each model, we decide to start the initial threshold value at 0, and to
increase 0.05 at each time until 0.95, since all the intervals of the models are between 0 and 1 except for
Resnik’s model, which is between 0 and infinite. To deal with this problem, we adopt the normalized
Resnik’s model (Equation 18) to replace Resnik’s model (Equation 7), because the former has the same
performance as the latter but the interval of the former is between 0 and 1. Subsequently, we obtain the
performance data for each model at each time of the variation of the threshold value.
Since the F-measure and F-measure (β=2) are two aggregated metrics, we decide to use them as the
primary benchmarks for seeking the optimal threshold value. Fig. 16 and Fig. 17 respectively show the
variation of F-measure values and the variation of F-measure (β=2) values of the four candidate models on
different threshold values.
Fig. 16. Variation of F-measure values of the four models on threshold values

Fig. 17. Variation of F-measure (β=2) values of the four models on threshold values
Based on the two figures above, we choose the optimal threshold value for each candidate model, on
which each model can obtain the highest F-measure value and F-measure (β=2) value. Following that, we
need to acquire the optimal threshold value for the proposed model. Owing to the fact that our model is
based on a weighted arithmetic mean, we also need to find out the optimal β value on which the model can
achieve the best performance. Fig. 18 and Fig. 19 respectively show the variation of F-measure values of
our model on threshold value and β value.
Fig. 18. Variation of F-measure values of Dong et al.’s model on threshold value and β value

Fig. 19. Variation of F-measure (β=2) values of Dong et al.’s model on threshold value and β value
Eventually, we choose the optimal threshold values for each model respectively based on the highest F-
measure value and the highest F-measure (β=2) value, which are shown in Tables 3 and 4. Subsequently,
we horizontally compare their performance based on the six indicators.
First of all, the performance of the five models on the highest F-measure value is depicted in Table 3. It
is observed that our model has a significant advantage over the other models in terms of precision, recall
and F-measure, in addition to holding the second position on mean average precision and fallout.
Second, the performance of the five models on the highest F-measure (β=2) value is displayed in Table 4.
Similar to Table 3, our model stands at first position on precision, recall and F-measure, and the second
position on mean average precision and fallout.
Based on the two comparisons, it can be deduced that our model performs better than the other models
in this experiment. Therefore, we primarily prove the proposed model by these experiments.
The reason that the statistical data are relatively low for these models is that we determine the answer set
for each concept based on human judgment. For a large number of concepts within the health service
ontology, the answer sets are empty, since they are unique and there are no logically similar concepts for
them. These concepts lower the average performance of these models.
Table 3. Performance of the five models on the highest F-measure value
Table 4 Performance of the five models on the highest F-measure (β=2) value
Model Name
Optimal
threshold value Precision
Mean Average
Precision Recall Fallout F-measure (β=2)
Rada’s model >0.5 13.57% 44.00% 52.41% 11.89% 33.33%
Resnik’s model >0.4 16.32% 46.45% 53.70% 11.99% 36.83%
Lin’s model >0.25 14.31% 47.30% 54.58% 12.46% 22.80%
Jiang and Conath’s model >0 17.81% 82.67% 24.52% 1.69% 34.92%
Dong et al.’s model (β=0.3) >0.15 30.64% 68.17% 71.12% 3.51% 56.26%
Model Name
Optimal
threshold value Precision
Mean Average
Precision Recall Fallout F-measure
Rada’s model >0.5 13.57% 44.00% 52.41% 11.89% 21.55%
Resnik’s model >0.9 25.60% 67.25% 34.50% 2.82% 29.39%
Lin’s model >0.35 18.79% 61.55% 43.13% 5.86% 26.17%
Jiang and Conath’s model >0.15 22.97% 90.68% 19.55% 0.80% 21.12%
Don
g
et al.’s model
(
β
=0.4
)
>0.25 40.23% 73.44% 54.26% 2.02% 46.20%

7. CONCLUSION
In this paper, by observing the features of the existing semantic similarity models, we find two limitations
within the models when applying them in the ontology environment, which are: 1) these models ignore the
context of relations; 2) these models ignore the context of ontology concepts. In order to resolve the two
issues, we design a novel solution, including an ontology conversion process and a hybrid semantic
similarity model. The ontology conversion process aims at encapsulating the context of relations and
ontology concepts into the body of a pseudo-concept, and transforming an ontology with a complicated
structure into a simple lightweight ontology. In order to cope with various properties, restrictions and
characteristics of properties in the OWL Lite/DL annotated semantic web documents, we define a set of
theorems for the conversion process. Next, we provide a hybrid semantic similarity model, which includes
an enhanced cosine correlation model to compute the similarity between two concepts from the perspective
of a pseudo-concept context, and a normalized Resnik’s model to calculate the similarity from the
perspective of the lightweight ontology structure. Eventually, we take the means of a weighed arithmetic
mean to combine the two similarity measures. In order to validate the model, we implement it in a large-
scale knowledge base – a health service ontology. Based on the six performance indicators adopted from
the IR field, we compare our model with the other four typical models – Rada’s model from the edge-based
models, Resnik’s model and Lin’s model from the node-based models and Jiang and Conath’s model from
the hybrid models. The experimental results show that our model has better performance than the other four
models, which preliminarily proves its feasibility.
Future works will concentrate mainly on the following three aspects: 1) we will evaluate our model
using other large scale knowledge bases; 2) we will enhance the semantic similarity model by considering
more factors for the similarity computation; 3) we will enhance the ontology conversion process to better
represent the features of the context of properties and restrictions and characteristics of properties.
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