Semantic Similarity based on Weighted Ontology - Geographical Information Systems: Trends and Technologies - page 303

Following the discrete uniform probability distribution mentioned
above, the weights of arcs along a path are equally probable and depend
on the number of belonging nodes. Accordingly, the weights of arcs of
longer paths are less than the weights of arcs of shorter paths. The benefi ts
of this approach consist in weighting differently both the sibling nodes
(e.g., Region , State , Department ) and nodes belonging to a path (e.g., Region ,
Province , Municipality ) that otherwise are not distinguished by uniform
probability distribution. In fact, according to the uniform probabilistic
approach the weights of Region , State , Department coincide and are equal
to 0.1667 (see Fig. 3), whereas conforming to the uniform probabilistic
weighted arc approach they are distinct and are equal to 0.0625, 0.08333,
and 0.125 respectively (see Fig. 4).
In accordance with the general theory of the standard argumentation
of information theory (Shannon 1948) a concept weight will be used to
determine its information content. The information content of a concept c
is defi ned as follows:
ic ( c ) = - log w ( c )
where w is the weight associated with the concept c in the reference
hierarchy. The basic intuition behind the use of the negative log likelihood
is that the more probable a concept is of appearing then the less information
it conveys, in other words, specialized concepts are more informative
than more general ones. Thus, as the weight of a concept increases the
informativeness decreases, hence, the more general a concept the lower its
information content.
Correspondingly, in Fig. 4, we observe that the weight of nodes at
the lower level of a path is less than the ones at the higher level. In fact,
the nodes at lower level represent more specifi ed parts of concepts with
respect to the concepts at higher level, e.g., Municipality is more specifi ed
(or detailed) part of Region with respect to Province . Thus, the probability
of a meronym is less than the probability of its holonym. Accordingly, the
information content of a low probable concept is higher than the information
content of a high probable concept. For instance, the information content
of Municipality ic ( Municipality ) = -log(0.00391) = 7.9986 is higher than
ics ( Province ) = - log(0.01563) = 5.9995. Similarly, the information content
of Province is higher than ic ( Region ) = -log(0.0625)=4.0.
We can observe in Fig. 4, as the probability-based weight increases in
the hierarchy in bottom-up direction, the information content decreases.
In other words, the information content increases in an opposite direction,
i.e., top-down.
With respect to this approach, a different method consists in taking into
account the weight of predecessor arcs of a given arc, which is called non-