Global Positioning System Reference
In-Depth Information
It represents the least abstract concept of the hierarchy that is more general
concept with respect to both
c
i
and
c
j
in the case of
Is-A
relation, or contains
both
c
i
and
c
j
in the case of
Part-of
relation.
In Fig. 1, an example of an
Is-A
hierarchy is shown, where for instance
the
lub
of the concepts
Seasonal_river
and
Aqueduct
is
River_system
. Whereas,
Fig. 2 represents a
Part-of
hierarchy, in which as an example
Country
is the
lub
of concepts
Municipality
and
Department
.
Defi nition
6: A
Weighted Reference Ontology
(
H
w
) is a pair:
H
w
=<
H
,
w
>
where
w
is a function defi ned on
C
, such that given a concept
c
ยข
C
,
w
(
c
)
is a rational number in the interval [0,1].
In this chapter, we focus on
Part-of
hierarchies, however the selected
approaches mentioned in the Introduction section can also be applied to
Is-A
hierarchies (Beeri 1990). Below the notions of
weighted
ontology according
to different weighting approaches are introduced.
Frequency-based approach
In the large majority of papers proposed in the literature, the assignment
of weights to the concepts of a reference hierarchy (or a taxonomy) is often
performed by using WordNet (see for instance; Kim and Candan 2006; Li
et al. 2003; Resnik 1995; Lin 1998; Budanitsky and Hirst 2006; Patwardhan
and Pedersen 2006). WordNet provides a measure of the
frequency
of the
concept. The
frequencies
of concepts are estimated using noun frequencies
from large text corpora, as for instance the Brown Corpus of American
English (Francis and Kucera 1979). Then, the
SemCor
project (Fellbaum et
al. 1997) made a step forward by linking subsections of Brown Corpus to
senses in the WordNet lexicon. According to
SemCor
, the total number of
observed instances of nouns is 88312.
In Fig. 3, for instance, WordNet has been used to assign weights to the
geographic classes. According to frequency-based approach, the
weight
of
the concept
c,
indicated as,
w
f
(
c
) is defi ned as follows:
freq
(
c
)
M
w
f
(
c
) =
where
freq
(
c
) is the frequency of the concept
c
, and
M
is the total number
of observed instances of nouns in the corpus. In Table 2, frequencies of
geographic classes according to WordNet 2.0 are illustrated. Note that, in
WordNet there are concepts for which the frequency is not given, such as
for instance
Department
, and
Municipality
. For this reason, in Table 2, the
frequencies of such concepts are assumed to be equal to 1. Another limitation
of WordNet is related to multi-word terms, for which the frequency are not
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