SEMANTICS-BASED SIMILARITY DECISIONS FOR
ONTOLOGIES
Anne Yun-An Chen, Dennis McLeod
University of Southern California, 941 W. 37th Place, Los Angeles, CA 90089-0781, U.S.A.
Keywords: Data mining, Ontology, Semantics, Similarity decision
Abstract: Many data representation structures, such as web site categories and domain ontologies, have been
established for semantic-based information search and retrieval on the web. These structures consist of
concepts and their interrelationships. Approaches to determine the similarity in semantics among concepts
in data representation structures have been developed in order to facilitate information retrieval and
recommendation processes. Some approaches are only suitable for similarity computations in pure tree
structures. Other approaches designed for the Directed Acyclic Graph structures yield high computational
complexity for online similarity decisions. In order to provide efficient similarity computations for data
representation structures, we propose a geometry-based solution. Similarity computations are based on
geometric properties. The similarity model is based on the proposed geometry-based solution, and the
online similarity computation is performed in a constant time.
1 INTRODUCTION
Data representation structures have been developed
to support online information search and retrieval.
Interconnections of concepts define the relationships
among the concepts, and hierarchical structures are
commonly employed data representation structures.
Examples of hierarchical structures are web site
directories, subject categories, web page links, and
some general or domain ontologies (Phillipi, 2004)
(De Lazzari, 2003). There exits ontologies that are
represented by Directed Acyclic Graph (DAG)
structures. Ontologies contain sufficient information
to facilitate information retrieval processes in order
to match user expectations of retrieved results
(Latifur, 2004).
Traversing DAG structures for similarity
decisions is complicated since there may be more
than one possible path from one concept node to
another. Several possible traversing paths indicate
the ambiguity of the similarity decision. Similarity
computations in DAG structures have been studied
in the filed of knowledge discovery in databases
(KDD) (Shekar, 2002).The relatedness of two items
is calculated by traversing all possible paths.
Traversing all possible paths costs O(|E|), |E| is the
number of edges. The maximum number of |E|
is
]2)2)(1([ −− nn
, where n is the number of
nodes in the structure. The computational
complexity can be expressed as O(n
2
) for online
computations.
A geometry-based solution is proposed to
provide systematic similarity computations,
uncomplicated online similarity decisions, and data
representation structure configurations. The
similarity is determined within the data
representation structure, and is decided with the
consideration of the direct inheriting relationship
quantity. The solution is also suitable for DAG
structures with simple adjustments. The proposed
solution enables the utilization of current data
representation structures. If the similarity
computation is required to be performed online to
support the information search or recommendation,
the data adaptation and the similarity model
construction is performed offline. The online
similarity computation cost O(c), c is a constant
.
2 GEOMETRIC-BASED DATA
ADAPTATION
Geometry enables the study of properties of
elements that remain invariant under specific
transformations. In the proposed geometric-based
solution, vertices are represented by points, and
edges are represented by vectors in geometric space.
443
Yun-An Chen A. and McLeod D. (2005).
SEMANTICS-BASED SIMILARITY DECISIONS FOR ONTOLOGIES.
In Proceedings of the Seventh International Conference on Enterprise Information Systems, pages 443-446
DOI: 10.5220/0002553604430446
Copyright
c
 SciTePress

The similarity can be decided based on the
geometric properties of coordination.
2.1 Data Adaptation
The data adaptation manipulates data representation
structures with defined geometric properties in a 3-
dimentional space. The assumption here is that the
structure for the similarity computations only has
one root node. If DAG structures are involved in the
data adaptation process, a virtual parent node of the
root nodes will be inserted before the data adaptation
begins. The proposed algorithm shown below
performs the data adaptation. The input is G {V, E},
where V are nodes (vertices) and E are edges. The
outputs are the coordinates of points and vectors
between points
.
while(not all edges are traversed)
{
Get the next available node;
If (current node is not marked as
VISITED)
{
Accumulate the minimum number of
edges to reach the root node as ID;
if(the plane of X=ID does not exist)
Create a plane X=ID;
//x representing the id value,
//y representing the next
//available incremental value, //and
z representing 1 larger //number
from the maximum z //value of the
previous plane.
Assign the x, y, z value of the
coordination to the current node;
Define the vector between the node
and its parent node;
Mark the current node as VISITED;
for (each plane X=value, value<x)
{
//x= value,
//y=the y value(s) of the
//parent(s)
//z= current z value.
Assign the mapping coordination
x, y, z;
}
}
else
{
if(the coordination has been
adjusted before)
Replace the adjusted
coordination to the original
coordination;
Calculate the difference between
the z-axis values of two parent
nodes of the visited node;
while(From the parent node with
larger z-axis value Z, not reach
the node has the same z-axis value
Z’ as the other parent node)
{
Change the z value of
mapping coordination for each
reached node of the same y-
axis value and its descendant
to Z’+[(z-Z’)/(difference +
1)];
for (each plane X=value,
value<x value of the new
parent)
{
//x= value,
//y=the y value(s) of
//the parent(s)
//z= current z value.
Assign the mapping
coordination x, y, z;
}
}
}
}
The data adaptation takes c
×
n
2
iterations, where
c is a constant and n is the total number of nodes.
The scale of the possible total number of objects in
the queue is O(n
2
), the number of edges minus the
number of the root nodes. The plane creation in the
3-dimensional space costs O(max (d’)), where d’ is
the minimum number of the edges to reach the root
node for the nodes in the structure. For a single-
rooted structure, the maximum number of operations
for the coordinate adjustment is the total number of
all possible edges. Again, the number is bounded by
n
2
. The final computational complexity for the
algorithm is O(n
2
).
3 SEMANTIC-BASED
SIMILARITY MODEL
The proposed semantic-based similarity model
introduces semantic-based operations to provide
answers to similarity decision problems. In this
similarity model, three operations are included. The
first operation is data adaptation, which is described
in detail in the previous section. The second
operation, the semantic-based grouping, provides the
foundation of efficient online similarity decision
processes. The third operation is to decide the
semantically similar groups and their priorities. In
the following sections, an approach using similarity
decisions based on fundamental properties of the
geometry embedded in the data representation
structures is proposed
.
3.1 Semantically Similar
Before the approach of similarity decisions is
introduced, definitions of similarity degrees must
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first be declared. First, a broad definition of the
similarity in semantics is declared below.
Definition 1: If two concepts as ending points
share the same starting point of the vector, the two
concepts are hierarchically similar.
If two concept nodes share the same starting
point of their vectors, the two nodes must have at
least one common parent node in the domain
ontology before the adaptation. Now, a narrow
definition of the similarity in semantics is declared.
Definition 2. If two concepts are hierarchically
similar and the z-axis values are the same, the two
concepts are semantically similar.
Having the same parent node does not imply
these two child nodes must have the same generality.
The reason is that one node may have more than one
parent node, and these parent nodes do not always
have the same generality
.
3.2 Semantic-based Grouping
Semantic-based grouping is introduced to utilize the
results of the geometry-based data adaptation and to
facilitate the online recommendation processes.
Semantic-based grouping means that groups which
contain semantically similar concepts are determined
based on the data adaptation results offline.
Grouping performed offline decreases the
computational complexity of the online similarity
decision making. Concepts that are semantically
similar are labelled as one group. Priorities are
assigned to each group according to the following
definition.
Definition 3: If any two concepts share n same
parent nodes, the priority of the two concepts is n
and higher than two concepts that share (n-1) parent
nodes
.
3.3 Online Similarity Decisions
A similarity decision process framework based on
the proposed similarity model consists of three
gradational approaches, locating semantically
similar concept groups, selecting candidates of
recommended concepts, and deciding the
recommended concept(s). Semantically similar
groups containing the concepts being queried are
first located. Offline sorting, based the priorities of
groups that have one common concept, enables the
online group locating to be completed in a constant
time of O(C
top
), where C
top
is the number of top
priority groups needed for deciding the
recommended concepts. The value of C
top
is decided
by the information system developers.
After all semantically similar groups are located,
concepts in these groups excluding the queried
concept are considered as the candidates of the
recommended concepts. The candidate(s) with the
highest priority will be selected to be recommended.
The goal of the selecting candidate approach is to
obtain the concept nodes with large similarity
degrees. A number C
limit
, where C
limit
is a constant, is
set to limit the number of selecting. In total, the
computational complexity of the online similarity
decision is O(C), where C is a constant
.
4 APPLICATIONS ON
ONTOLOGY
4.1 Earthquake Domain Ontology
In order to access the tremendous amount of
heterogeneous geoscience data, a semantic metadata
management system and wrappers for web services
Figure 1: Partial Earthquake Science Domain Ontology
SEMANTIC-BASED SIMILARITY DECISIONS FOR ONTOLOGIES
445

are required. The domain ontology is the core of the
metadata management system (Chen, 2003) and is
illustrated in Figure 1. In the following sections, we
demonstrate an example of the similarity model
application
.
4.1.1 Application of the Similarity Model
The proposed approach to determine similarity
decisions consists of three elements, the geometric-
based data adaptation, the geometric-based
similarity definition, and the semantic-based
similarity model. The results of the approach are
listed in Table 1
.
Table 1: Results of grouping and priority defining
Group of Concepts Priority
Earth 1
Crust 1
Fault 1
Segment, San Andreas, Sierra Madre,
Lone Tree, Kane Spring
1
Carrizo, Cholame, Coachella, Mojave,
North Coast, Cucamonga, San Fernando
1
Carrizo, Cholame, Coachella, Mojave,
North Coast
2
Cucamonga, San Fernando 2
4.1.2 Recommendation Processes
The recommended concepts associated with queried
concepts and decided by the proposed similarity
model are demonstrated in the following case.
Case 1: If the queried concept is Cucamonga, the
recommended concept is San Fernando. It is because
the group these concepts belong to has a higher
priority. The assigned priority is 2, and the value of
C
top
here is set to 1.The other group containing the
concept Cucamonga only has the priority of 1
.
5 CONCLUSION
A semantic-based similarity model is proposed to
solve similarity decision problems in data
representation structures. The goal of the model
development is to perform similarity computations
in spontaneous and unambiguous similarity
decisions. The data adaptation process is developed
to utilize geometric properties. Based on the results
of the data adaptation process, the similarity degree
is decided by geometric properties. The semantic-
based similarity decision model consists of offline
computations and online operations. The offline
computations include semantically similar grouping
for concept nodes and priority computations for
semantically similar groups. Performing grouping
and computing priorities offline enables the
reduction in the computational complexity of online
similarity decisions. Online similarity decisions are
completed by a sequence of three approaches:
locating semantically similar concept groups,
selecting candidates of recommended concepts, and
deciding the recommended concept(s). The proposed
similarity model serves as a good foundation for
recommendation processes due to the combination
of uncomplicated approaches and results in constant-
timed computations
.
ACKNOWLEDGEMENT
This work was supported by NASA's Computational
Technologies Project. Portions of this work were
carried out by the Jet Propulsion Laboratory,
California Institute of Technology under contract
with NASA
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