Global Positioning System Reference
In-Depth Information
In formula (4),which is borrowed from the Tversky's model (see S Tversky
discussed in the State of the Art section) S , and T are description sets of the
classes s, t , respectively, S
T , S - T ( T - S ) are the set-theory intersection
and difference of the sets S, T , respectively, and 0w α ( s, t ) w1 is a function
defi ning the “relative importance” of the non-common attributes of the
classes. This function is essentially defi ned in terms of the distance among
the classes s , and t the class representing their least upper bound in the
hierarchy. Such a distance is given by the number of arcs along the shortest
path between classes, and is defi ned as follows:
{
d ( s, lub )
d ( s, t )
d ( s, lub ) w d ( t, lub )
α ( s, t ) =
d ( s, lub )
d ( s, t )
1 -
d ( s, lub ) d ( t, lub )
where d ( s, t ) = d ( s, lub ) + d ( t, lub ).
For instance, in Fig. 2, α ( Municipality, County ) = 0.4 because the lub of
these concepts is Country .
In the MDSM approach, the weights w att , w func , w part indicate the relevance
of attributes, functions and hierarchical parts, respectively. They are defi ned
on the basis of two different approaches, namely variability and commonality .
These approaches are recalled in the following, where the term “feature”
in accordance with (Rodriguez and Egenhofer 2004) stands for attributes,
functions or parts.
According to the variability approach, the relevance of a feature is
related to the feature's informativeness, therefore the feature's relevance
decreases if it is shared by most of geographic classes in the knowledge
base. Whereas, according to the commonality approach, high frequency of
a feature corresponds to high relevance. Given a geographic knowledge
base, assume q is a type of feature. Then, let P q and P q (where v stands for
variability and c for commonality , respectively) be defi ned as follows:
P q = 1 - m ¹
i=1
Oi
nm
(5)
P q = m ¹
i=1
Oi
nm
= 1 - P q
(6)
where O i is the number of occurrences of a feature in the geographic
knowledge base, n is the number of geographic classes and m is the number
of distinct features in the geographic knowledge base. Since in this chapter,
we deal with the evaluation of the relevance of both the hierarchical (parts)
and attribute components of a geographical knowledge base, we focus on
determining the weights w att , w part .
 
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