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<Paper uid="W98-0703">
  <Title>I I I i I i I I I I I I I I I I I ! I Word Sense Disambiguation based on Semantic Density</Title>
  <Section position="4" start_page="17" end_page="17" type="metho">
    <SectionTitle>
3 Ranking the possible senses of
</SectionTitle>
    <Paragraph position="0"> the noun In order to improve the precision of determining the conceptual density between a verb and a noun, the senses of the noun should be ranked, such as to indicate with a reasonable accuracy the first possible senses that it might have.</Paragraph>
    <Paragraph position="1"> The approach we considered for this task is the use of unsupervised statistical methods on large texts. The larger the collection of texts, the bigger is the probability to provide an accurate ranking of senses. As the biggest number of texts electronically stored - and thus favoring an automatic processing - is contained on the Web, we thought of using the Internet as a source of corpora for ranking the senses of the words.</Paragraph>
    <Paragraph position="2"> This first step of our method takes into consideration verb-noun pairs V - N, and it creates pairs in which the verb remains constant, i.e. V, and the noun is replaced by the words in its similarity lists. Using WordNet, a similarity list is created for each sense of the noun. and it contains: the words from the noun synset and the words from the noun hypernym synset.</Paragraph>
    <Paragraph position="3"> Algorithm 1 Input: untagged verb - noun pair Output: ranking of noun senses  Procedure: 1. Form a similarity list for each noun sense.  Consider, for example, that the noun N has m senses. This means that N appears in m similarity lists,</Paragraph>
    <Paragraph position="5"> (N', .V r~l), N &amp;quot;(~) ..... N &amp;quot;~ k&amp;quot; )) where ,V l, N &amp;quot;~ ..... N&amp;quot; represent the different senses of :V, and ,V i(') represents the synonym number s of the sense N i of the noun N as defined in WordNet.</Paragraph>
    <Paragraph position="6">  2. Form verb - noun pairs. The pairs that may be formed are:</Paragraph>
    <Paragraph position="8"> . Search the \[nternet and rank senses. A search performed on the Internet for each of these groups will indicate a ranking over the possible senses of the noun N.</Paragraph>
    <Paragraph position="9"> In our experiments we used (AhaVista) since it is one of the most powerful search engines currently available.</Paragraph>
    <Paragraph position="11"> Using the operators provided by AltaVista, the verb-noun groups derived above can be expressed in two query-forms: of the result we obtained in ranking the noun senses using the Internet</Paragraph>
    <Paragraph position="13"> where the asterisk (*) is used as a wildcard indicating that we want to find all words containing a match for the specified pattern of letters.</Paragraph>
    <Paragraph position="14"> Using one of these queries, we can get the number of hits for each sense i of the noun and this provides a ranking of the m senses of the noun as they relate with the verb V.</Paragraph>
    <Paragraph position="15"> We tested this method for 80 verb-noun pairs extracted from SemCor 1.5 of the Brown corpus, i Using query form (a) as an input to the search engine, we obtained an accuracy of 83% in providing a ranking over the noun senses, such as the sense indicated in SemCor was one of the first two senses in this classification. \[n Table 1, we present a sample of the results we obtained. The column Result in this table presents the ranking over the noun senses: a I in this column means that the sense indicated in SemCor was also indicated by our method: 2 means that the sense indicated in SemCor was in top two of the sense ranking provided by our method; similarly, 3 or 4 indicates that the sense of the noun, as specified in :~emCor, was in the top three, respectively four, of 1;his sense ranking.</Paragraph>
    <Paragraph position="16"> We u.,ed also the query form (b), but the results we obtained have been proved to be similar; using the operator NEAR, a bigger number of hits is reported, but the sense ranking remains the same.</Paragraph>
    <Paragraph position="17"> It is i:ateresting to observe that even we are creating queries starting with a verb-noun pair, it is ITh~: verb-noun pairs have been extracted from the file br-aO:.</Paragraph>
    <Paragraph position="18"> not guaranteed that the search on the web will identify only words linked by such a lexical relation. We based our idea on the fact that: (1) the noun directly following a verb is highly probable to be an object of the verb (as in the expression &amp;quot;Verb* Noun*&amp;quot;) and (2) for our method, we are actually interested in determining possible senses of a verb and a noun that can share a common context.</Paragraph>
  </Section>
  <Section position="5" start_page="17" end_page="19" type="metho">
    <SectionTitle>
4 Determining the conceptual
</SectionTitle>
    <Paragraph position="0"> density between verbs and nouns A measure of the relatedness between words can be a knowledge source for several decisions in the NLP applications. The conceptual density between verbs and nouns seems difficult to determine, without large corpora or a without a machine-readable dictionary having semantic links between verbs and nouns. Such semantic links can be traced however if we consider the glosses for the verbs, which are providing a possible context of a verb.</Paragraph>
    <Paragraph position="1"> Algorithm 2 Input: untagged verb - noun pair and a ranking of noun senses (as determined by Algorithm 1) Output: sense tagged verb - noun pair  Procedure: 1. Given a verb-noun pair V - N, determine all the possible senses for the verb and the noun, by using WordNet. Let us denote them by &lt; vl, v2 ..... t,~ &gt; and &lt; nt, n2 ..... nl &gt; respectively. null 2. Using the method described in section 3, the senses of the noun are ranked. Only the first two possible senses indicated by this step will be considered.</Paragraph>
    <Paragraph position="2"> 3. For each possible pair Vi -- n), the conceptual density is computed as follows:  (a) extract all the glosses from the sub-hierarchy including vi (the rationale of the method used to determine these sub-hierarchies is explained below) (b) Determine the nouns from these glosses. These constitute the noun-context of the verb. All these nouns are stored together with the level of the associated verb within the sub-hierarchy of vi.</Paragraph>
    <Paragraph position="3"> (c) Determine the nouns from the sub-hierarchy including ni.</Paragraph>
    <Paragraph position="4"> (d) Determine the number Cij of common concepts between the nouns obtained at (b) and the nouns obtained at (c).</Paragraph>
    <Paragraph position="5"> 4. The most suitable combinations between the  senses of the verb and the noun vi - nj are the ones that provide the biggest values for Cij. In order to determine the sub-hierarchies that should be used for vl and nj, we used statistics provided by SemCor, a sense tagged version of the Brown corpus (Francis and Kucera, 1967) (Miller, Leacock et al., 1993), containing 250,000 words. Each word (noun, verb, adjective, adverb) is ineluded in a synset within a hierarchy. The tops of these hierarchies denominate the class of the word. The sense in SemCor for a word W is indicated by the class C of the word W, and the sense of the word within the class C. For example, the SemCor entry: &lt;el cndfdone pos=PIN le~ma=investigation gnsn=l lexsn= 1 : 09: O0 : : &gt; invest igat ion&lt;/ef&gt; indicates: word: investigation part of speech: common noun sense in WordNet: 1 A statistic measure performed on SemCor, indicates the following probabilities for the sense of a word within a class:  a class As shown in Table 2, the class of the noun indicates with a probability of 85% a correct sense 1 within that class.</Paragraph>
    <Paragraph position="6"> Thus, for this algorithm, we consider for a noun the hierarchy including the noun (if the class of the noun ni is C', then the method considers all the nouns from the class C).</Paragraph>
    <Paragraph position="7"> This does not work for the verbs, as the probability to indicate a correct sense knowing the class is much smaller (only 60%). For this reason, and based on the experiments we computed, the sub-hierarchy  including a verb vi is determined as follows: (i) consider the hypernym hi of the verb oi and (ii) consider the hierarchy having hi as top.</Paragraph>
    <Paragraph position="8"> It is necessary to consider a bigger hierarchy then just the one provided by synonyms and direct hyponyms, since providing accuracy in a metric computation needs large corpora. As we replaced the corpora with the glosses, better results are achieved if more glosses are considered. Still, we do not have to enlarge too much the context, in order not to miss the correct answers.</Paragraph>
    <Section position="1" start_page="19" end_page="19" type="sub_section">
      <SectionTitle>
Conceptual Density Metric
</SectionTitle>
      <Paragraph position="0"> For determining the conceptual density between a noun ni and a verb vj, the algorithm considers:  * the list of nouns sv~ associated with the glosses of the verbs within the hierarchy determined by hi: (svk,w~), where: - hj is the hypernym of vj - w~ is the level in this hierarchy * the list of nouns snt within the class of ni : (snt)  The common words between these two lists (svk,wk) and (snt) will produce a list of common concepts with the associated weights cdij &lt; w~ &gt;. The conceptual density between rli and vj is given by the formula:</Paragraph>
      <Paragraph position="2"> where: * Icdijl is the number of common concepts between the hierarchies of ni and uj * w~ are the weights associated with the nouns from the noun-context of the verb vj * desci is the total number of words within the hierarchy of noun nl As the nouns with a big hierarchy tend to indicate a big value for Icdijl, the weighted sum of common concepts has to be normalized in respect with the dimension of the noun hierarchy. This is estimated as the logarithm of the total number of descendants in the hierarchy (i.e. Io9(desci)).</Paragraph>
      <Paragraph position="3"> We also took into consideration other metrics,  like: (2) The number of common concepts between the noun and verb hierarchies, without considering the weights.</Paragraph>
      <Paragraph position="4"> (3) A weighted summation of the common concepts  between the noun and verb hierarchies, as indicated in (1), but without a normalization in rapport with the noun hierarchy.</Paragraph>
      <Paragraph position="6"> We considered also the metrics indicated in (Agirre and Rigau, 1995). But after running the program on several examples, the formula indicated in (1) provided the best results.</Paragraph>
      <Paragraph position="7"> A possible improvement to the metric (1) is to consider the weights for the levels in the noun hierarchy, in addition to the levels in the verb hierarchy.</Paragraph>
    </Section>
  </Section>
  <Section position="6" start_page="19" end_page="20" type="metho">
    <SectionTitle>
5 An example
</SectionTitle>
    <Paragraph position="0"> Consider as example of a verb-noun pair the phrase revise lauC/. The verb revise has two possible senses in WordNet 1.5: Sense 1 revise, make revisions in gloss: (revise a thesis, for example) =~ rewrite, write differently, alter by writing gloss: (&amp;quot;The student rewrote his thesis&amp;quot;) Sense 2 re tool, revise =~ reorganize, shake up, organize an The noun law has 7 possible senses Sense 1 law, jurisprudence gloss: (the collection of rules imposed by authority; ~civilization presupposes respect for the law&amp;quot;) collection, aggregation, accumulation, assemblage gloss: (several things grouped together) Sense 2 law gloss: (one of a set of rules governing a particular activity or a legal document setting forth such a rule; &amp;quot;there is a law against kidnapping&amp;quot; ) ~, rule, prescript gloss: (prescribed guide for conduct or action) =~ legal document, legal instrument, ofl~icial document, instrument Sense 3 law, natural law gloss: (a rule or body of rules ofconduct inherent in human nature and essential to or binding upon human society) =~ concept, conception gloss: (an abstract or general idea inferred or derived from specific instances) Sense 4 law, law of nature gloss: (a generalization based on recurring facts or events (in science or mathematics etc): &amp;quot;the laws of thermodynamics) concept, conception gloss: (an abstract or general idea inferred or derived from specific instances) Sense 5 jurisprudence, law, legal philosophy gloss: (the branch of philosophy concerned with the law) philosophy gloss: (the rational investigation of questions about existence and knowledge and ethics) Sense 6 police, police force, constabulary, law gloss: (the force or policemen and officer~; &amp;quot;the law came looking for him&amp;quot; } =~ force, personnel gloss: (group of people willing to obey orders} Sense T law. practice of law gloss: Ithe learned profession that is mastered by graduate study in a law school and that is responsible for the judicial system; &amp;quot;he studied law at Yale&amp;quot;)  :*. learned profession gloss: (one of the three professions traditionally believed to require advanced \[earning and high principles) null We searched on lnternet, using AltaVista, for all possible pairs V-N that may be created using revise and the words from the similarity lists of law. Over the seven possible senses for this noun, the first step of our method indicated the following ranking (we indicate the number of hits between parenthesis):law#e(2829), !aw#3(648), law#4(640), law#6(397), 1aw#1(224), 1aw#5(37), taw#7(0). Thus, only the sense # and #3 of the noun law are eligible to be used for the next algorithm.</Paragraph>
    <Paragraph position="1"> For each of the two senses of the verb, we determined the noun-context, including the nouns from the glosses in the sub-hierarchy of the verb, and the associated weights.</Paragraph>
    <Paragraph position="2"> For each of the two possible senses of the noun, we determined the nouns from the class of each sense. In Table 3, we present: (1) the values obtained for the combinations of different senses, i.e. the number of common concepts between the verb and noun hierarchies- \[cdq\[ (columns 2-3); (2) the summations of the weights associated with each noun within the noun-context of the verb vj (columns 4-5); (3) the total number of nouns within the hierarchy of each sense hi, i.e. desci (columns 6-7); (4) the conceptual density Cq for each pair ni - vj, derived using the formula presented above (columns 8-9).</Paragraph>
    <Paragraph position="3"> ~ edl, l\[ 3 weights desC/, C, 1 4 5 6 7 8 9</Paragraph>
    <Paragraph position="5"> sity and the conceptual density C,j In this table: - vi indicates the sense number i of verb revise - ni indicates the sense number i of noun law The biggest value for conceptual density is given</Paragraph>
    <Paragraph position="7"> This combination of verb-noun senses 2 appears in SemCor, file br-a01.</Paragraph>
  </Section>
  <Section position="7" start_page="20" end_page="20" type="metho">
    <SectionTitle>
6 Tests against SemCor
</SectionTitle>
    <Paragraph position="0"> We tested this method by using verb-noun pairs from SemCor. A randomly selected sample from the entire table with 80 pairs is presented in Table 4.</Paragraph>
    <Paragraph position="1"> For each pair verb-noun, we indicate the sense of the verb (column B). the sense of the noun (column C), as they result from SemCor; the total number of possible senses for both the verb (column D)</Paragraph>
    <Paragraph position="3"> these cases, the NEAR operator should be used for the first step of this algorithm).</Paragraph>
    <Paragraph position="4"> 2. The number of words considered at a time can be increased, from two to three, four or even more words.</Paragraph>
  </Section>
  <Section position="8" start_page="20" end_page="20" type="metho">
    <SectionTitle>
7 Conclusion
</SectionTitle>
    <Paragraph position="0"> In this paper, we have presented a method for WSD that is based on measuring the conceptual density between words using WordNet. The metric proposed may be further improved by considering the weights for verbs as well as for nouns. The senses of the words are ranked, and an user may select the first choice or the first few choices, depending upon the application. We have also proposed to use the Internet as a source of statistics on a raw corpora.</Paragraph>
    <Paragraph position="1"> The method extends well to considering more than two words at a time, and also for all parts of speech covered by WordNet.</Paragraph>
    <Paragraph position="2"> It is difficult to compare the precision obtained by this method with other methods, since we consider here the collective meaning of two or more words, while most of other methods consider one word at a time. However, an estimation can be done by extracting the square root of the accuracy for a pair of verb-noun words; and that is 76.15% for the first choice, 83.66% for the first two choices and 85.44% for the first three choices. Since the disambiguation precision for nouns is usually higher than for verbs, those numbers provide only an average.</Paragraph>
  </Section>
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