Global Positioning System Reference
In-Depth Information
set of boys and a set of girls, respectively. A candidate set of pairs defi nes a
possible set of marriages (when polygamy is not allowed) (Galil 1986).
Defi nition
11: Let
m
1
,
m
2
be the names of two geographic classes as in the
previous defi nition, such that
h
w
k
. The
tuple similarity
of
m
1
,
m
2
,
indicated
as,
tSim
(
m
1
,
m
2
) is defi ned as follows:
ݐܵ݅݉ሺ݉
ଵ
ǡ݉
ଶ
ሻൌ
ଵ
ቀ
݉ܽݔ
ሺǡሻא
ቁ
(7)
where
ics
is the information content similarity,
P
(
m
1
,
m
2
) is the set of
candidate sets of pairs of
m
1
,
m
2
, and V(
m
1
,
a
), V(
m
2
,
b
) are the types associated
with
a, b
in the classes
m
1
,
m
2
, respectively.
Example
9: Let us consider the geographic classes
Municipality
(
k
= 5) and
County
(
h
= 3). A possible set of pairs that maximizes the formula (7) is:
ܤאܲሺ݉
ଵ
ǡ݉
ଶ
ሻ
σ
݅ܿݏሺܽǡܾሻכ݅ܿݏሺ߬ሺ݉
ଵ
ǡܽሻǡ߬ሺ݉
ଶ
ǡܾሻሻ
ሼ൏ܿݑ݊ݐݎݕܥ݀݁ǡܿݑ݊ݐݕܫܦǡ൏݄ܾ݅݊ܽ݅ݐܽ݊ݐǡݑ݈ܽݐ݅݊ǡ
൏ܽݎ݁ܽǡݏݑݎ݂ܽܿ݁ሽ
According to Defi nition 9, we have:
ics
(
inhabitant, population
) =
ics
(
area,
surface
)=1
and the same holds for related types, i.e.,
ics
(
string, string
) =
ics
(
integer,
integer
)=1, whereas
ics
(
countryCode, countyID
) = 0.
Thus
tSim
(
Municipality, County
) =
5
= 0.4.
Note that two possible sets that maximizes the sum above each contains the
pair (
identity, countyID
) and (
councilHead, countyID
) in place of (
countryCode,
countyID
).
In fact
ics
(
identity, countyID
) = 0,
ics
(
councilHead, countyID
) = 0.
An important parameter in the similarity of geographic classes is
related to the similarity of their geometric components, as defi ned in the
following:
Defi nition
12: Let
G
i
and
G
j
be sets of geometric types. The similarity of
geometric types, indicated as N
Sim
(
G
i
,
G
j
), is defi ned as below:
ߣܵ݅݉ሺܩ
ǡܩ
ሻ
=1 if
ܩ
תܩ
്
ߣܵ݅݉ሺܩ
ǡܩ
ሻ
=0 otherwise
For instance, in the case of geographic classes in Example 9, the sets of
geometric types of
Municipality
and
County
are {
point, polygon
} and {
polygon
},
respectively. Thus, N
Sim
(
Municipality, County
)=1.
Defi nition
13: Let
m
1
=< {
a
1
:
t
1
, ...,
a
k
:
t
h
},
G
1
>,
h
1 and
m
2
=< {
b
1
:
t
1
, ...,
b
k
:
t
k
},
G
2
>,
k
1 be the names of two classes of the geographic knowledge base
K
E
= (
C, A, Cls
),
H
w
be a weighted
Part-of
hierarchy, and a
SynSet
K
= {
S
1
, ...,
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