Global Positioning System Reference
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Finally, the measures calculated according to the variability and
commonality approaches,
MDSM
v
and
MDSM
c
, respectively, are:
ܯܦܵܯ
௩
(
Municipality,
County
)=
ݓ
௧
௩
כܵ
௧௧
ሺ
ܯݑ݈݊݅ܿ݅ܽ݅ݐݕǡܥݑ݊ݐݕ
ሻ
+
ݓ
௧
௩
כ
ܵ
௧
ሺܯݑ݈݊݅ܿ݅ܽ݅ݐݕǡܥݑ݊ݐݕሻ
=0.470*0.526+0.530*0=0.247
ܯܦܵܯ
(
Municipality,
County
)=
ݓ
௧
כܵ
௧௧
ሺ
ܯݑ݈݊݅ܿ݅ܽ݅ݐݕǡܥݑ݊ݐݕ
ሻ
+
ݓ
௧
כ
ܵ
௧
ሺܯݑ݈݊݅ܿ݅ܽ݅ݐݕǡܥݑ݊ݐݕሻ
=0.599*0.526+0.401*0=0.315
Combined approach
Most of similarity methods proposed in the literature are based on the
hierarchical structure of concepts, in contrast with the work of psychologists
who typically focus on concept features (or attributes) (Rodriguez and
Egenhofer 2004). Recently, there has been a growing effort to capture both
the concept similarity within the reference ontology, and the similarity of
properties of geographic classes. For instance, the proposal in (Formica
and Pourabbas 2009), called
GSim
, is an approach that combines both such
similarities. In particular, it focus on geographic partition hierarchies, and
the attribute similarity (here referred to as
tuple
similarity) of geographic
classes. In this mentioned paper, the concepts of the reference ontology (or
hierarchy) have been weighted by using
WordNet
taxonomy concepts.
The
GSim
method has been defi ned by revisiting, extending, and
integrating two approaches, which are the
information content (ics)
approach
as defi ned in Lin (1998), and a method for tuple similarity which is based
on the
maximum weighted matching
problem in bipartite graphs (Kuhn 1955).
The fi rst approach regards the formal defi nition of information content
approach, which is composed of three points (see below, Defi nition 9),
i.e., point (i) that states the
ics
of two concept names is equal to 1 if they
coincide or are synonyms, otherwise in all the other cases (point (iii)), their
similarity is equal to zero. In point (ii), the information content similarity
of hierarchically related concepts, as discussed in the previous section, is
formally defi ned.
Defi nition
9: Given a geographic knowledge base
K
E
=
(
C, A, Cls
), a weighted
reference hierarchy
H
w
and a
SynSet
K
= {
S
1
,...,
S
n
},
n
0 for
K
E
. Let us consider
the sets
T
of atomic types, as defi ned previously. Given
m
1
,
m
2
¢
C
A
T
,
the
information content similarity
of
m
1
,
m
2
, indicated as
ics
(
m
1
,
m
2
), is defi ned
as follows:
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