Global Positioning System Reference
In-Depth Information
maximum information content shared by the classes. Given two classes
c
i
and
c
j
, the similarity between them is defi ned by the information content
of the concept that is the least upper bound (
lub
) of
c
i
, c
j
in the hierarchy,
and is given as follows:
Sim
R
= - log
w
(
lub
(
c
i
, c
j
))
In the Resnik's approach,
w
(
c
) is calculated by estimating the probability
of occurrence of the class in a large text corpora.
For instance, let us consider weights
w
f
of geographic classes shown
in Fig. 3. Let us consider the geographic classes
Region
and
County
. Since
their
lub
is
Country
, the following holds:
Sim
R
= - log
w
f
(
Country
) = 8.3218
Successively, concept similarity has been refi ned by Lin (1998) as the
maximum information content shared by the concepts (
Sim
R
) divided by
the information contents of the comparing concepts as follows:
2 log
w
(
lub
(
c
i
, c
j
))
log
w
(
c
i
) + log
w
(
c
j
)
Sim
Lin
(
c
i
, c
j
) =
For instance, the
Sim
Lin
of the classes mentioned in the previous
example is:
2 log
w
f
(
Country
)
log
w
f
(
Region
) + log
w
f
(
County
)
Sim
Lin
(
Region, County
) =
2
*
8.3218
10.3642 + 11.3429
=
= 0.76674
Observation on weights
As anticipated in the Probability-based approach subsection of the previous
section, depending on the reference ontology, sometimes the weight
associated with whole
(
holonym
)
and its parts (meronyms) coincide. For
instance, referring to the weighted ontology shown in Fig. 3, we observe
that the weight associated with
Region, Province
, and
Municipality
is equal to
0.1667. Thus, the similarity of pairs (
Region, State
), (
Province, State
) coincide
too. In fact,
Sim
Lin
(
Region, State
) =
Sim
Lin
(
Province, State
) = 0.3869. Thus,
uniform probabilistic approach is not appropriate for weighting concepts
of reference ontologies similar to the one shown in Fig. 3.
However, according to the uniform probabilistic weighted arc approach,
we observe that the similarity of the pairs mentioned above is different. In
fact, they are:
Sim
Lin
(
Region, State
) =0.5274,
Sim
Lin
(
Province, State
) =0.4173.
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