Global Positioning System Reference
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labeled with a weight equal to 1/( k - 1). We proceed to label arcs in the
remaining paths. If an arc is labeled only by one weight, then this will be
assigned to the arc. Otherwise, in the case of an arc labeled by more than
one weight, the minimum weight among the labeled ones will be assigned
to the arc. In the following the defi nition of uniform probabilistic weighted
arc is given
Defi nition 8: Given a concept c i , let c i be a part (or meronym) of c i -1 . The
weight of c i is given by the following formula:
w pa ( c i ) = w pa ( c i -1 ) * w a ( i -1, i )
(2)
where, w a ( i -1, i ) indicates the weight of arc connecting the concepts c i -1 , c i .
Example 6: Let us consider Fig. 4. We identify three paths, which are
Path1: < Top, Country, Department >
Path2: < Top, Country, State, County >
Path3: < Top, Country, Region, Province, Municipality >
We observe that the number of arcs for paths is 2, 3, and 4, respectively.
Hence, the uniform weights of arcs are 1/2, 1/3, and 1/4 along each path,
as well. In this approach, weights of arcs along a given path are equal. In
other words, the weight of each arc w a ( i -1, i ) is constant and it is equal to 1/
( k - 1), where k is the number of nodes of the belonging path. In Fig. 4, the
arc connecting To p and Country nodes are labeled with three weights, 0.5,
0.33, and 0.25. Thus, minimum value is assigned as weight to this arc.
w pa =1
Top
w a =m in(0.5,0.33,0.25)
Country
w pa =0.25
w a =0.5
w a =0.25
w a =0.33
w pa =0.08333
w pa =0.0625
State
Region
w pa =0.125
Department
w a =0.33
w a =0.25
Province
w pa =0.01563
County
w pa =0.02778
w a =0.25
Municipality
w pa =0.00391
Fig. 4. Hierarchy weighted by uniform probabilistic weighted arc approach.
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