Onto.PT: Towards the Automatic Construction of a Lexical Ontology ...

116 Chapter 7. Moving from term-based to synset-based relations
All the candidate synsets with the highest rp are added to a new set, C. If
rp < θ, a predefined threshold, a is not attached. Otherwise, a is attached to the
synset(s) of C with the highest ni. Term b is attached using the same procedure,
but fixing a.
The RP algorithm is illustrated in figure 7.2, where it is used to ontologise the
tb-triple {a R1 b}, given the candidate synsets and the network in figure 7.1 1 .
rpA1 = 3/4* rpB1 = 3/3*
rpA2 = 2/3 rpB2 = 2/3
rpA3 = 1/3 rpB3 = 1/2
rpA4 = 4/6
max(rp(Ai, {a, R1, b})) = 3/4 → A1
max(rp(Bi, {a, R1, b})) = 3/3 → B1
resulting sb-triple = {A1 R1 B1}
Figure 7.2: Using RP to select the suitable synsets for ontologising {a R1 b}, given
the candidate synsets and the network N in figure 7.1.
Average Cosine (AC): Assuming that related concepts are described by words
related to the same concepts, this algorithm exploits all the relations in N to select
the most similar pair of candidate synsets. A term adjacency matrix M(|V | × |V |)
is first created based on N, where |V | is the number of nodes (terms). If the terms
in indexes i and j are connected (related), Mij = 1, otherwise, Mij = 0.
In order to ontologise a and b, the most similar pair of synsets, Ai ∈ A and
Bj ∈ B, is selected according to the adjacencies of the terms they include. The
similarity between Ai and Bj, represented by the adjacency vectors of their terms,
Ai = {ai0, ...,ain}, n = |Ai| and Bj = { bj0, ..., bjm}, m = |Bj|, is given by the average
similarity of each term aik with each term bjl, in N:
sim(Ai, Bj) =
|Ai|
|Bj|
k=1 l=1
cos(aik, bjl)
|Ai||Bj|
(7.2)
While this expression has been used to find similar nouns in a corpus
(Caraballo, 1999), we adapted it to measure the similarity of two synsets, represented
as the adjacency vectors of their terms.
The AC ontologising algorithm is illustrated in figure 7.3, where it is used to
ontologise the tb-triple {a R1 b}, given the sample candidate synsets and the sample
network in figure 7.1. The example shows that, in opposition to the RP algorithm,
AC uses all the relations in the network (R1, R2 and R3), and not just those of the
same type of the tb-triple to ontologise (R1).
1 For the sake of simplicity, we ignored the 1+log2(|Ai|) in the denominator of the rp expression,
and considered it to be just the size of the synset, |Ai|.