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

7.1. Ontologising algorithms 117
Adjacency matrix M, for the network in figure 7.1:
a b c d e f g h i j l
a 1 1 0 0 0 1 1 1 0 0 0
b 1 1 1 1 1 0 0 0 0 0 1
c 0 1 1 0 0 0 1 1 0 0 0
d 0 1 0 1 0 0 0 0 0 0 0
e 0 1 0 0 1 1 0 0 0 0 1
f 1 0 0 0 1 1 0 0 0 0 1
g 1 0 1 0 0 0 1 0 1 0 0
h 1 0 1 0 0 0 0 1 1 1 0
i 0 0 0 0 0 0 1 1 1 0 0
j 0 0 0 0 0 0 0 1 0 1 0
l 0 1 0 0 1 1 0 0 0 0 1
Cosine values for each pair:
B1 B2 B3
A1 3.15/12 ≈ 0.26 1.80/12 ≈ 0.15 1.35/8 ≈ 0.17
A2 2.44/9 ≈ 0.27 3.54/9 ≈ 0.39 * 1.59/6 ≈ 0.26
A3 1.21/9 ≈ 0.13 0.81/9 ≈ 0.09 0.37/6 ≈ 0.06
A4 5.48/18 ≈ 0.30 3.16/18 ≈ 0.18 1.96/12 ≈ 0.16
max(sim(Ai, Bj)) ≈ 0.39 → resulting sb-triple = {A2 R1 B2}
Figure 7.3: Using AC to select the suitable synsets for ontologising {a R1 b}, given
the candidate synsets and the network N in figure 7.1.
Related Proportion + Average Cosine (RP+AC): This algorithm combines
RP and AC. If RP cannot select a suitable synset for a or b, because one, or both,
the selected synsets have rp < θ, a selected threshold, AC is used.
Number of Triples (NT): Pairs of candidate synsets, Ai ∈ A and Bj ∈ B, are
scored according to the number of tb-triples of type R, present in N, between any
of their terms. In other words, the pair that maximises nt(Ai, Bj) is selected:
nt(Ai, Bj) =
|Ai|
|Bj|
k=1 l=1
E(aik, bjl, R) ∈ E
log2(|Ai||Bj|)
(7.3)
As it is easier to find tb-triples between terms in larger synsets, this expression
considers the size of synsets. However, in order to minimise the negative impact of
very large synsets, a logarithm is applied to the multiplication of the synsets’ size.
The NT ontologising algorithm is illustrated in figure 7.4, where it is used to
ontologise the tb-triple {a R1 b}, given the sample candidate synsets in figure 7.1
and the sample network in the same figure 2 .
2 For the sake of the clarity, we ignored the log2 in the denominator of the nt(Ai, Bj) expression,
and considered it to be just |Ai||Bj|.