Global Positioning System Reference
In-Depth Information
on approaches in which the weights and the similarity between concepts
may take any value between 0 and 1.
Probability-based approach
The probabilistic approach is based on a uniform probabilistic distribution
along the reference hierarchy. The root of the hierarchy, referred to as
To p
has
weight equal to 1 (i.e.,
w
p
(
To p
)=1), and weights are assigned to the concepts
of the hierarchy according to a top-down approach, as follows.
Defi nition
7: Given a concept
c
, let
c
be a part (or meronym) of
c'
,
w
p
(
c
) is
equal to the probability of
c'
divided by number of parts, for short
P
, of
c'
as follows:
w
p
(
c'
)
|P
(
c'
)
|
w
p
(
c
) =
(1)
This approach is based on the discrete uniform distribution notion
in probability theory and statistics (Balakrishnan and Nevzorov 2005),
according to which a fi nite number of values are equally likely to be
observed, i.e., each one of
n
values has equal probability 1/
n
. Accordingly,
the rationale behind the defi nition above is that all parts (or meronyms) of
a holonym are equally probable.
Example
5: Assume the root of the hierarchy shown in Fig. 3 has two
parts. Thus, the weight associated with
Country
is 0.5 (according to Eq.
(1),
w
p
(
Country
) =
w
p
(
To p
)
2
)
.
Now, let us consider the concept
Region.
The
associated
w
p
is 0.1667 because
Country
has three parts (i.e.,
Region
,
State
,
Department
).
In Fig. 3, the uniform probabilistic-based weights associated with the
geographic classes are indicated. As we can observe nodes (except the
root node and the
Country
node) have only one part. It means that the
weight associated with whole and its parts coincide (e.g., (
Region, Province
),
(
Province, Municipality
), (
State, County
)). As we will see in the next section,
the similarity of the above mentioned concepts (e.g.,
Region, Province
) with
a given concept (e.g.,
State
) coincide as well. Thus, similar cases will not be
distinguished by using the uniform probabilistic approach.
In order to distinguish such cases, we propose a different probabilistic
approach to assign weights as described below. In this approach, called
uniform probabilistic weighted arc
, the weight of nodes is calculated on the
basis of the weights of its predecessor
node
and
arc
. The weights assigned
according to this approach are shown by
w
pa
. Starting from the Top node
(we assume
w
pa
(
To p
) = 1), we distinguish different paths along its successor
nodes. Thus, given a path defi ned by
k
nodes, each arc along this path is
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