For clustering purposes, word senses are repre­sented as topic signatures (Lin and Hovy, 2000). Thus, for each word sense s we define a vector Algorithm 1 Clustering-based approach for the dis­ambiguation of the set of words W in the textual context T_

Input: The finite set of words W and the textual context T.

Output: The disambiguated word senses.

Let S be the set of all senses of words in W, and i = 0; repeat (t1 : a1,...,tm : am), where each ti is a Word­Net term highly correlated to s with an association weight <7i. The set of signature terms for a word sense includes all its WordNet hyponyms, its di­rectly related terms (including coordinated terms) and their filtered and lemmatized glosses. To weight signature terms, the tf-idf statistics is used, con­sidering each word as a collection and its senses as its of documents. Topic signatures of senses form a Vector Space Model similar to those defined in In­formation Retrieval Systems. In this way, they can be compared with measures such as cosine, Dice and Jaccard (Salton et al., 1975).

In (Anaya-Sanchez et al., 2006), it is shown that this kind of WordNet-based signatures outperform those Web-based ones developed by the Ixa Re­search Group in the disambiguation of nouns.

Sense clustering is carried out by the Extended Star Clustering Algorithm (Gil et al., 2003), which builds star-shaped and overlapped clusters. Each cluster consists of a star and its satellites, where the star is the sense with the highest connectivity of the clus­ter, and the satellites are those senses connected with the star. The connectivity is defined in terms of the ß0-similarity graph, which is obtained using the co­sine similarity measure between topic signatures and the minimum similarity threshold ß0. The way this clustering algorithm relates word senses resembles the manner in which syntactic and discourse relation links textual elements.

Once clustering is performed over the senses of words in W, a set of sense clusters is obtained. As some clusters can be more appropriate to describe the semantics of W than others, they are ranked ac­cording to a measure w.r.t the textual context T.

As we represent the context T in the same vector space that the topic signatures of senses, the follow­ing function can be used to score a cluster of senses g regarding T :

where words(g) denotes the set of words having senses in g, g is the centroid of g (computed as the barycenter of the cluster), and number(s) is the WordNet number of sense s according to its corre­sponding word.

Then, we rank all clusters by using the lexico­graphic order of their scores w.r.t. the above func­tion.

Once the clusters have been ranked, they are or­derly processed to select clusters for covering the words in W. A cluster g is selected if it contains at least one sense of an uncovered word and other senses corresponding to covered words are included in the current selected clusters. If g does not con­tain any sense of uncovered words it is discarded. Otherwise, g is inserted into a queue Q. Finally, if the selected clusters do not cover W, clusters in Q adding senses of uncovered words are chosen until all words are covered.

As a result of the filtering process, a set of senses for all the words in W is obtained (i.e. the union of all the selected clusters). Each word in W that has only a sense in such a set is considered disambiguated. If some word still remains ambiguous, we must refine the clustering process to get stronger cohesive clus­ters of senses. In this case, all the remaining senses must be clustered again but raising the ß0 threshold.

In this subsection we illustrate the use of our pro­posal in the disambiguation of the content words appearing in the sentence "The runner won the marathon". In this example, the set of disam­biguating words W includes the nouns runner and marathon, and the verb win (lemma of the verbal form won). Also, we consider that the context is the vector T = (runner : 1,win : 1, marathon : 1). The rest of words are not considered because they are meaningless. As we use WordNet 2.1, we regard that the correct senses for the context are runner#6, win#1 and marathon#2.

Figure 1 graphically depicts the disambiguation process carried out by our method. The boxes in the figure represent the obtained clusters, which are sorted regarding the ranking function (scores are un­der the boxes).

Initially, all word senses are clustered using ßo=0.049 (the 90th-percentile of the pairwise similarities between the senses). It can be seen in the figure that the first cluster comprises the sense runner#6 (the star), which is the sense refering to a trained athlete who competes in foot races, and runner#4, which is the other sense of runner related with sports. Also, it includes the sense win#1 that concerns to the victory in a race or competition, and marathon#2 that refers to a footrace. It can be easily appreciated that this first cluster includes senses that cover the set of disambiguating words. Hence, it is selected by the filter and all other clusters are

marathon # 3

discarded. After this step, S is updated with the set {runner#6, runner#4, win#1, marathon#2}.

In this point of the process, the senses of S do not disambiguate W because the noun runner has two senses in S. Therefore, the sttoping criterion does not hold because neither |S| = |W| and ß0(2) = 0.104 = 1. Consequently, a new cluster distribution must be obtained using the current set S.

The boxes in the bottom of Figure 1 represent the new clusters. In this case, all clusters are sin­gles. Obviously, the cluster containing the sense runner#4 is discarded because the cluster that in­cludes the sense runner#6 overlaps better with the context, and therefore precedes it in the order.

Then, the final set of selected senses is S = {runner#6, win#1, marathon#2}, which in­cludes only one sense for each word in W.

Firstly, it is worth mentioning that we do not use the coarse-grained inventory provided by the com­petition for this task. Indeed, our approach can be viewed as a method to build such a coarse-grained inventory as it clusters tightly related senses.

Each W was defined as the set of all tagged words belonging to the sentence under consideration. Ta­ble 3.1 shows the official results obtained by our sys­tem.

As it can be appreciated, the effectiveness of our method was around the 70%, except in the fifth test document (d005), which is an excerpt ofstories about Italian painters.

Similar to previous task, we included into each W those tagged words of the disambiguating sentence. However, as the set of tagged words per sentence was verb-plentiful, with very few nouns, we ex­panded W with the rest of nouns and adjectives of the sentence.

Table 3.2 summarizes the results (split by word categories) obtained in this subtask. The second col­umn of the table shows the number of disambiguat-ing word occurrences.

As we can see, in this subtask only nouns and verbs were required to be disambiguated, and over­all, verbs predominate over nouns. The poor per­formance obtained by verbs (w.r.t. nouns) can be explained by its high polysemy degree and its rela­tively small number of relations in WordNet.