Global Positioning System Reference
In-Depth Information
Following the approach of non-uniform probabilistic weighted arc, we
obtain:
Sim
Lin
(
Region, State
) =0.3581,
Sim
Lin
(
Province, State
) =0.233.
Feature-based method
Feature-based methods have been conceived to measure the similarity
between concepts as a linear combination of the measures of their common
and distinctive features or attributes (Tversky 1977). Common features
tend to increase the similarity, and conversely, non-common features tend
to decrease the similarity of two concepts. One of the well-known feature-
based approaches is Dice's function (Maarek et al. 1991; Castano et al.
1998). According to such approach, given two concepts, say
c
i
, and
c
j
,
each
described by a set of features, say
F
(
c
i
),
F
(
c
j
), respectively, their similarity
is defi ned as follows:
2
|B
(
c
i
, c
j
)
|
|F
(
c
i
)
| + |F
(
c
j
)
|
Dice
(
c
i
, c
j
) =
where
B
(
c
i
, c
j
) = {(
x, y
)
|x
¢
F
(
c
i
),
y
¢
F
(
c
j
),
x, y
¢
D
⊑
A f f
},
A f f
is the set of
sets of attributes showing affi nity that is computed similar to the maximum
weighted matching problem in bipartite graphs (Kuhn 1955), and for any
set
X
,
|X|
indicates the cardinality of
X
.
For instance, let us consider
Municipality,
and
County
in Table 1. The
pairs of attributes showing affi nity are (
population
,
inhabitant
), (
area
,
surface
).
Thus:
2
*
2
5 + 3
Dice
(
Municipality, County
) =
= 0.5
A different approach based on features is the proposal of Rodriguez
and Egenhofer (2004), called
Matching-Distance Similarity Measure
(MDSM
for short). This method is a weighted sum of the similarity measures for
parts
,
functions
and
attributes
, which are the distinguishing features of spatial
entity classes. Given two classes, say
s
and
t,
their similarity according to
MDSM, indicated as
MDSM
(
s, t
) is given by the following formula:
MDSM
(
s, t
) =
w
att
*
S
att
(
s, t
) +
w
func
*
S
func
(
s, t
) +
w
part
*
S
part
(
s, t
)
(3)
where
w
att
,
w
func
,
w
part
, are the weights of similarity vales for attributes,
functions and parts, respectively, such that
w
att
+
w
func
+
w
part
= 1 (defi ned
below), and
S
q
(
s, t
),
q
standing for attributes (
att
), functions (
func
), and parts
(
part
) is defi ned as follows:
S
q
(
s, t
)
|S
∩
T|
=
(4)
|S
∩
T| + α
(
s, t
)
|S
-
T| +
(1 -
α
(
s, t
))
|T
-
S|
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