A Wordnet from the Ground Up

96 Chapter 3. Discovering Semantic Relatednessprobabilities, we used a slightly modified version of Leacock’s similarity measure(Agirre and Edmonds, 2006):()P ath(s 1 , s 2 )sim(s 1 , s 2 ) = − log, (3.9)max sa,sb P ath(s a , s b )P ath(a, b) is the length of a path between two synsets in plWordNet.Except for synset similarity, we follow (Lin and Pantel, 2002, Pantel, 2003) strictlyin other aspects of word-sense evaluation. Synset similarity is used to define thesimilarity between a word w and a synset s. Let S(w) be a set of wordnet synsetsincluding w (its senses). The similarity between s and w is defined as follows:simW (s, w) = max sim(s, t) (3.10)t∈S(w)The similarity of a synset s (a sense recorded in a wordnet) and a group of LUs c(extracted sense) is defined as the average similarity of LUs belonging to c. LU groupsextracted by CBC have no strict limits. Their members are of different similarity to thecorresponding committee (sense pattern). The core of the LU group is defined in (Linand Pantel, 2002, Pantel, 2003) via a threshold κ 26 on the number of LUs belongingto the core. Let also c κ be the core of c – a subset of κ most similar members of c’scommittee. The similarity of c and s is defined as follows:∑w∈csimC(s, c) =κsimW (s, u)(3.11)κWe assume that a group c corresponds to a correct sense of w ifmax simC(s, c) ≥ θ (3.12)s∈S(w)The wordnet sense of LU w, corresponding to the sense of w represented bya lemma group c is defined as a synset which maximizes the value in formula 3.12:arg max simC(s, c) (3.13)s∈S(w)The question arises why this evaluation procedure is so indirect. Why do we notcompare the cores of the LU groups with wordnet synsets? The answer is seeminglysimple. Both in Polish and in English, certain matches are hard to obtain. LU groupsare indirectly based on the MSR used. They do not have clear limits, and still showsome closeness to a sense, but not to a strictly defined sense. On the other hand,wordnet synsets also have a substantial level of subjectivity in their definitions, especiallywhen they are intended to describe concepts, which are not directly observable26 We changed the original symbol k to κ so as not to confuse it with k in the algorithm.