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<Paper uid="P98-2232">
  <Title>Combination of an Automatic and an Interactive Disambiguation Method</Title>
  <Section position="3" start_page="0" end_page="1423" type="metho">
    <SectionTitle>
2 Preconditions for Disambiguation
</SectionTitle>
    <Paragraph position="0"> This section describes preconditions for disambiguation and methods of the disamlfiguation.</Paragraph>
    <Paragraph position="1"> In this paper, the disambiguation for ambiguous words means that all ambiguous ones in an input sentence a.re disambiguated. Describing it. formally, the disambiguation is to decide one element of the following MS.</Paragraph>
    <Paragraph position="3"> where an input sentence contains ! ambiguous words. Mi means the set of lneanings in the ambiguous word wi.</Paragraph>
    <Paragraph position="4"> Each disambiguation method has preconditions as follows:</Paragraph>
    <Section position="1" start_page="0" end_page="1423" type="sub_section">
      <SectionTitle>
Interactive Disambiguation
</SectionTitle>
      <Paragraph position="0"> * In the interaction, the system shows explanations for each meaning of an ambiguous word to a user, who selects one explanation from them.</Paragraph>
      <Paragraph position="1">  * The system can calculate the probability where a user selects the right explanation.</Paragraph>
    </Section>
    <Section position="2" start_page="1423" end_page="1423" type="sub_section">
      <SectionTitle>
Automatic Disambiguation
</SectionTitle>
      <Paragraph position="0"> * The occurrence probabilities for each candidate can be calculated for preference.</Paragraph>
      <Paragraph position="1"> * The result is the candidate with the maximum occurrence probability.</Paragraph>
      <Paragraph position="2"> To show the iuformation mentioned above, candidates are expressed by the tree in Figure 1. This tree is an example in the case that an input sentence is &amp;quot;I saw a star.&amp;quot;, which contains two ambiguous words 'see' and 'star' and each word has two meanings.</Paragraph>
      <Paragraph position="3"> root 771~1 1 77112 1711n  one ambiguous word in an input sentence The accuracy of the interactive disambiguatiou /~ntr and that of the automatic disambiguation Pauto are defined as follows: root.</Paragraph>
      <Paragraph position="5"> The depth of the tree expresses the order of disanfl)iguation. In Figure 1, the auabiguities are resolved in the order from 'see' to 'star'. The occurfence probability is calculated at each leaf node by the automatic disambiguation method. For exampie, PH expresses the probability for the candidate {see_l,star_l}. Furthermore, the accuracy of interaction is also calculated at the leaf node by the interactive disalnbiguation method. Pd~.l is the probability where the meanillg of 'star' is 'staLl' and tim system shows explanations of 'star_l', 'star_2' for 'star' to a user a.nd (s)he selects the explanation of 'star_2'. At. Nodes besides leaf ones, only the accuracy of interaction is calculated.</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="1423" end_page="1424" type="metho">
    <SectionTitle>
3 The Condition of Executing the
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="1423" end_page="1423" type="sub_section">
      <SectionTitle>
Interactive Disambiguation
3.1 Basic Idea
</SectionTitle>
      <Paragraph position="0"> At each node besides leaf ones, the disambiguation system decides which disambiguation method is used. Basically, the interactive disambiguation is executed when its accuracy is higher than the accuracy of the automatic disambiguation. First of all, let us consider the case where an input sentence contains one ambiguous word that has ~, meanings.</Paragraph>
      <Paragraph position="1"> Figure 2 shows the tree of candidates for this case.</Paragraph>
      <Paragraph position="3"> The interactive disambiguation is executed, when the following condition is satisfied.</Paragraph>
    </Section>
    <Section position="2" start_page="1423" end_page="1423" type="sub_section">
      <SectionTitle>
Pintr &gt; Pauto
</SectionTitle>
      <Paragraph position="0"> Considering tile condition more carefully, the accuracy of tile interactive disambigualion is iufluenced by the explanations that are showu t.o users.</Paragraph>
      <Paragraph position="1"> Thus tim accuracy may be improved by limiting to show some explanations to users. For example, this may be caused when the accuracy of roll is very low and a user may select mll wrongly by the higher similarity of the explanation for 11111 to other explanations. The autonmtic disambiguation corresponds to showing only one explanation to users in the interactive disanabiguation. Therefore the condition of executing the interactive disambiguatiou can be defined as the exceptional case of the limitation.</Paragraph>
    </Section>
    <Section position="3" start_page="1423" end_page="1424" type="sub_section">
      <SectionTitle>
3.2 The Accuracy at a Node
</SectionTitle>
      <Paragraph position="0"> In the case that the number of alnbiguous words is one as Figure 2, the accuracy of the deeper nodes below the root node needs not to be decided because they are leaf nodes. When more than two ambiguous words exist in an input sentence, a node may often have one that is not a leaf one. To calculate the accuracy of such a node, it is necessary to determine what kind of disambiguation will be executed at the deeper nodes. For instance, the disambiguation system has to fix each accuracy of node 'see_l' and 'see_2' in Figure 1 to calculate the accuracy of the root node. Therefore, the definition of the accuracy at any node i is the recursive one. The accuracy of the interactive disambiguation Pintr(i) and that of the automatic disambiguation P~,to(i) at node i is defined as follows:</Paragraph>
      <Paragraph position="2"> where M is the set of the node directly under node i, pd(m\[M) is the accuracy of the interactive disambiguation at node m, that is, the probability that a user selects m provided that the system shows explanations for all the elements of M to him(her).</Paragraph>
      <Paragraph position="3"> Pr(m) is the accuracy at node m and the definition is as follows:</Paragraph>
      <Paragraph position="5"> (if the automatic disambiguation is executed at node m) Poccur(m) (if m is a leaf node) where/)occur(m) is tile occurrence probability of the candidate that includes nodes between the root node alld Ilode 7/l.</Paragraph>
      <Paragraph position="6"> When tile following condition is satisfied, the illteractive disanlbiguation is executed at node i.</Paragraph>
      <Paragraph position="8"/>
    </Section>
    <Section position="4" start_page="1424" end_page="1424" type="sub_section">
      <SectionTitle>
3.3 The Limitation of Explanations
</SectionTitle>
      <Paragraph position="0"> Ill user interaction, tile presentation of many explanations gives users trouble t.o select, one explanation.</Paragraph>
      <Paragraph position="1"> So it. is desirable that tile disambiguation system shows fewer exl)lanation to users, if possible. In this section, we describe the condition where the number of explanations is limited without losing the accuracy of the analyzed result.</Paragraph>
      <Paragraph position="2"> By formula (1), the accuracy of the interactive disanlbiguation Piaster in the case of limiting the set of explanations AI ~ is defined as follows:</Paragraph>
      <Paragraph position="4"> disambiguation is executed at. node i. Therefore, formula (4) implies fornmla (3).</Paragraph>
      <Paragraph position="5"> 4 Determination of the Order of</Paragraph>
    </Section>
    <Section position="5" start_page="1424" end_page="1424" type="sub_section">
      <SectionTitle>
Disambiguation
4.1 Procedure
</SectionTitle>
      <Paragraph position="0"> up to here, we have discussed ~l:amt r and Pluto under a certain order of disambiguation. Ill this section, we describe a procedure to decide the order of disambiguation where the accuracy is maximum.</Paragraph>
      <Paragraph position="1"> The accuracy of the analyzed result may be different in each order of disambiguation, This is the reason that the disambiguation of one ambiguous word leads to constrain the meaning of other ambiguous ones. Therefore, the contents of the interaction may differ from each order of disambiguation. The order with the maximum accuracy is obtained in the following procedure:  1. Calculating each occurrence probal)ility of candidate for tile analyzed result by the automatic disambiguation method.</Paragraph>
      <Paragraph position="2"> 2. Obtaining the accuracy in each order of (lisambiguation based on the method described in the previous sections.</Paragraph>
      <Paragraph position="3"> 3. Disanlbiguating by the order with the maximum accuracy.</Paragraph>
    </Section>
    <Section position="6" start_page="1424" end_page="1424" type="sub_section">
      <SectionTitle>
4.2 Example
</SectionTitle>
      <Paragraph position="0"> Ill this section, we illustrate the determination of executing the interactive disambiguatioll and the order of disanlbiguation. The values at leaf nodes are the occurrence probabilities. Tile accuracy of the interactive disalnbiguation is 0.9 at the any nodes. Since the number of ambiguous words is two, the number of the order of disambiguation is 2! as shown in</Paragraph>
      <Paragraph position="2"> To begin with, we intend to calculate what kind of disambiguation is executed at node 'star_l' and 'star_2', ill Figure 3. By fornmla (1), (2), ~nt,.(see-1) and Pluto(see-I) are as follows (since both ambiguous words have two meanings, P\[ntr(i)</Paragraph>
      <Paragraph position="4"> tomatic disambiguation is executed at. node see_l.</Paragraph>
      <Paragraph position="5"> Oil the other hand, at node see_2, P,,,t,.(see_2) and</Paragraph>
      <Paragraph position="7"> system interacts with users at this node.</Paragraph>
      <Paragraph position="8"> By the result of the above, Pi,t,.(root) and Pa,to(root) are as follows:</Paragraph>
      <Paragraph position="10"> Therefore, the interactive disambiguation is executed at. the root. node because of Pint,.( root ) &gt; P~to( rOot ), and P~(root) = 0.837.</Paragraph>
      <Paragraph position="11"> Next, let us explain the case of Figure 4. Calculating the same way as Figure 3, the interactive disambiguation is executed in any node besides leaf ones, and P/,t, (root), P~,to (root) are a.s follows:</Paragraph>
      <Paragraph position="13"> P,.(root) becomes 0.81. Comparing with P~(root) of each order, P~(root) of Figure 3 is greater than that of Figure 4. Thus the system interacts with users against 'see' in the first, place.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="1424" end_page="1424" type="metho">
    <SectionTitle>
5 Experiments
</SectionTitle>
    <Paragraph position="0"> We applied the proposed method(abbreviated as MP) to the disambiguation of trees of ca lldidates that are made for experiments, and compared it with the method (abbreviated as MA) that executes interaction in all nodes.</Paragraph>
    <Paragraph position="1"> We set the following properties to the tree of candidates. null * the number of ambiguous words included in an input sentence * the mlmber of meanings in an ambiguous word * the occurrence probability of candidates To assign an occurrence probability to each candidate, a raudom value is given to each candidate above all, and each value is divided by the sum of values given to all candidates.</Paragraph>
    <Paragraph position="2"> Figure 5, 6 show the accuracy at the root node and the number of interaction, respectively. In these figures, a mark '+' indicates results of MI ). Each of them is the average of 300 trees. A mark &amp;quot;*&amp;quot; indicates results of MA. Because MA does not prescribe the order of disambiguation, the result of each tree is the average of all the orders.</Paragraph>
    <Paragraph position="3">  The horizontal axis means the property of the tree. Each Alphabet in the value of the horizontal axis stands for the number of ambiguous words in a tree and the nunlber of meanings of a word as follows:  For instance, '2 x 4' shows that there are two ambiguous words ill a tree and one ambiguous word has two meanings and another word has four meanings. The lmmber in the value of the x-axis represents the number of the candidate whose occurrence probability is not zero. Two marks, &amp;quot;+' and '-' mean that the accuracy of interactioll is 0.9, 0.85 respectively.</Paragraph>
  </Section>
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