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<Paper uid="W99-0510">
  <Title>References</Title>
  <Section position="4" start_page="69" end_page="69" type="metho">
    <SectionTitle>
3 Experiments
</SectionTitle>
    <Paragraph position="0"> The basic idea of the matching m to find the dmtance (similarity) between a node in EDIt and a node m WordNet There could be several strategins for defining a distance between two nodes, ~e will use the words attached to each node and its parent, child and grandchild m the computatmn We did not use the descmptmns of concepts As a prehmmary experiment, we restricted the number of nodes to be considered, because both ontologms are big We used the nodes at the top 5 levels (distance from the top is at most 5) and deleted nodes which have no English words and no descendents In EDIt (some EDIt nodes have only Japanese words) This left 14,712 nodes In EDIt and 5,185 m WordNet Even with these restriction, the number of possible pmrmgs Is 76,281,720 Our target m to find good matches among them</Paragraph>
  </Section>
  <Section position="5" start_page="69" end_page="69" type="metho">
    <SectionTitle>
3 1 Definition of Distance
</SectionTitle>
    <Paragraph position="0"> The dmtance between nodes is defined based on the notion which ~s commonly used, the dine co-efficient Assume the node N1 m ontologyl has nl words and N~ m ontology2 has n2 words, and there are m words m common The dice coefficmnt (DC) is defined as follows</Paragraph>
    <Paragraph position="2"> Now we define the basic distance as 1 minus the ~alue The smaller the distance, the closer the two</Paragraph>
    <Paragraph position="4"> We now define the distance of two nodes (N1,N~.) based on the basra dlstance definition The words m parents, children and glandchildren are also used Such nodes are taken as a bag of nodes, le only one set of words is created for each category regardless of the number of node~ Such a bag of nodes is represented as N parent and so on The distance of each category is calculated just hke the basic d~stance In the following equation, cat should be replaced by parent, ztsel/, chzld and gchdd (for grandchild)</Paragraph>
    <Paragraph position="6"> Then interpolation is used to merge the four basic distances in order to keep the range from 0 to 1 We Introduce four coefficients cParent,cttsel/,acMld,c gch~ld tO define the node dls-</Paragraph>
    <Paragraph position="8"> cParent &amp;quot;1&amp;quot; cttself &amp;quot;f&amp;quot; cChtld + C gch'ld : 1 (2) The coefficients (cent's) will be the lraportant factor in the experiments As will be described m the next section, we use several combinations of the coefficients to observe which mformation ts important</Paragraph>
  </Section>
  <Section position="6" start_page="69" end_page="70" type="metho">
    <SectionTitle>
3 2 Experiments
</SectionTitle>
    <Paragraph position="0"> We conducted eight experiments using different combinations of the coefficients The first expemment uses only the reformation in the nodes themselves, while other expemments use the node and parent, the node and children, or all four sets Table 1 shows the coefficient combinations used m the expemments  Before descmblng the e~aluatlon results, some interesting anal~ ses are presented m thin sectmn These analyses do not concern directly the evaluatlon of the experiment, but indicate the natme of the expemments Ol the nature of the ontolog~es Number of outputs We used a threshold to resulct the nuInber of outputs If the distance ~s greater than 0 9, the result is not generated Table 2 shows the number of outputs m each experiment Itecall that there are 76,281,720-possible pairings of nodes It is interesting to see that the numbers are almost the same The number of outputs in E'cperlment-4 is shghtly smaller, we believe thin is because the weight asmgned to the nodes themsel~es, wluch gl~es the greatest contmbutmn, ~s low  The numbers are around 10,000, which represents 0 013% of the possible matches This suggests that there is a posslblllty of narrowing down the matches to be examined by a human, as the distance 0 9 ,s very large and the number of outputs ,s so small To prove th,s assumption, we have to conduct an evaluatmn to see ff there are good matches which were not generated Th,s ,s beyond the evaluatmn m thls paper, because it reqmres manual matching from scratch We will discuss this later</Paragraph>
    <Section position="1" start_page="70" end_page="70" type="sub_section">
      <SectionTitle>
Complete Match
</SectionTitle>
      <Paragraph position="0"> We can find the number of complete matches (which have exactly the same word(s)) by countmg the pmrs w~th d,stance 0 0 m Expenment-1 The number of complete matches is 1778, whlch ,s qmte large compared to the number of nodes under conslderatmn m WordNet (about 5,000) Also, by counting up the number of pmrs w,th distance</Paragraph>
      <Paragraph position="2"> matches whmh are complete matches where the parents also have the same words The number of parent-complete matches is 1 This is surprisingly small, even cons,dermg that we used only subsets of the 0ntologms The only parent-match is the  followingparent Invertebrate child arthropod Naturally people mlght guess that there would be more parent-complete matches For example, the name of a mammal might be a plaus,ble candidate (where the parent is &amp;quot;mammal&amp;quot; and child is, for example, &amp;quot;elephant&amp;quot;) However, this is not the case &amp;quot;Elephant&amp;quot; and &amp;quot;mammal&amp;quot; appear as follows (unrelated nodes are not sho~n)  Thls is one of the typlcal problems of ontolog} deslgn, how detail concepts should be mtrocuced Also, there is a translatlon problem m EDR, ,e sometimes there ,s words or a descnptmn m only one language There are some other &amp;quot;reasons why the number of parent-matches ,s so small * Some nodes m EDR have no words assoclated wlth them Thls is how the EDR Class,ficatlon Dmtlonary was deslgned It ~s based on the classfficat,on of words into some pre-defined boxes, and not creating hmrarchy of words It would be better to use the concept descnptlons of the dlctlonary, although it is not clear how to compare a s)nset (set of words) and a descnptlon Also, we mlght be able to use mformatlon written m Japanese when there ,s no Enghsh word but there are Japanese words * WordNet uses a synset to represent a node, whereas EDR's node Is pnmarlly represented by a descriptlon, there could be differences caused by thls The average numbers of words m a node are also different There were no chlldren-matches, whmh are complete matches where the words m the child nodes are also the same The closest matches m  children anomallstlc year, lunar year, school year, academlc year, solar year, troplcal year, astronomlcal year, equinoctial year (There are actually 4 child nodes )</Paragraph>
    </Section>
  </Section>
  <Section position="7" start_page="70" end_page="71" type="metho">
    <SectionTitle>
3 2 2 Evaluatmn
</SectionTitle>
    <Paragraph position="0"> As ~t ~s lmposs~ble to evaluate all the results, ~e selected four ranges (rank 1 to 20, 501 to 520, 2001 to 2020, and 9001 to 9020) and the data m these ranges was evaluated manually E~aluatmn ~as done by putting the matches into three categories  cluding partml matches and ambiguous cases b3 the manual evaluatmn However, the number of results m th~s category was not so large, so ~t should not affeSt the overall evaluatmn Table 3 shows the evaluatmn result The columns represent the four ranges and the each row represents one of the e,ght experiments An element has</Paragraph>
    <Paragraph position="2"> three numbers, corresponding to the categorms A, B and C, separated by &amp;quot;/&amp;quot; We can't make a direct comparison to other methods For example, while (Utlyama and Hashlda 1997) also used EDR and WordNet, they used only.connected components and we i/v/pose d the level restnctmn However, relative comparisons among our 8 experiments ar, e meaningful and important We will discuss them m the next section</Paragraph>
  </Section>
  <Section position="8" start_page="71" end_page="72" type="metho">
    <SectionTitle>
3 3 Dmcussmn
</SectionTitle>
    <Paragraph position="0"> Using only the nodes themselves (Exp-1) In Experiment-i, only the words m the nodes bemg compared are used The evaluatmn result was not very good For example, there are only 3 matches of category A m the highest range Based on an exammatmn of the results, we observed that this is due to word polysemy Even ff two nodes have a word m common, the word could have several meanings, and hence the corresponding nodes could have different meamngs For example, the word &amp;quot;love&amp;quot; can mean &amp;quot;emotion&amp;quot; or &amp;quot;no point in tenms&amp;quot; To see how the results we obtained m~ght arise, suppose a word has 4 senses in ontology1 and 5 m ontology2, and there are 3 senses which are the same m the' two ontologms Then there are 20 pairings of the senses and out of them only3 can be judged as category A Although this is just an assumptmn, the reahty m~ght not be that far from this explanation based on the observation of the result Adding chdd nodes (Exp-2,3,4) In Experiment-2,3 and 4, we used the mformatmn of the nodes themselves and their child nodes The evaluatmn results for Experiment-2 and 3 are the same, both of them have 6 A's in the h~ghest range The number is twine that in Expenment-1 This improvement is due to dlsamblguatmn of polysemous words For example, the same sense of a polysemous word might have similar words in the child nodes, whereas it might be rare that different senses have the same words m the two ontologms In Experiment-4, we put more weight on child nodes rather than the nodes themselves This experiment was conducted based on the assumptmn that the number of words m child nodes may be much larger than the number of words in the nodes themselves However, th~s turns out to give a degradation at the higher range Observing the result, the matches at the h~gher range have ~er~ few words m the child nodes If the number of chdd nodes are small in both ontologms and they have many m common, the d~stance between the nodes becomes extremely small Th~s could be both beneficml and harmful It can p,ck up some matches which could not be found m Experiment1, but the matches could be good or bad ones The followmg example is a good one which is actually found at the ninth rank m Experiment-4 EDIt parent(*) No Engllsh word, J-descrlptlon &amp;quot;target anlmals huntlng or flshlng&amp;quot; chlldren game, k111 WordNet pareni; (*) prey, quarry children game Adding parent nodes (Exp-5) In Experiment-5, the words in the nodes themselves and their parent nodes are used It can be naturally thought that the words in the parent nodes are useful to dlsamblguate polysemous words The result confirmed this In the highest range, category A has 10 matches out of 20 which ,s three t,mes as much as m Experiment-I, and twice that m Experiment-2 and 3 Using parents, self and chddren (Exp-6,7) In Expernnent-6 and 7 ~olds in parent, self and child nodes are used with different welghtmgs All e~aluaUon results are ~dentlcal e&lt;cept the lowest range, and these have the largest number of A's at the hlghest range among all of the experiments This mdmates that three sources together is better than any two or an~ single source of reformation Adding grandchdd nodes (Exp-8) Finally, m Experiment-8, words m all four kinds of nodes, parent, self, child and grandchild, are used The evaluation result is the same as that m  Experiment-6, and we could not see improvement by adding grandchild information Actually, by observing the result, we can see that the information at the grandchild level is not so useful Observing the evaluation process From the evaluation process, we understand that a human uses not only the four kinds of mformatmn, but also mformatmn ,n grandparent or the successor's nodes Some ,mprovement rmght be obta, ned if we used such mformatmn Also, we m,ght be able to achmve more improvement by using sibhng nodes, and the result of distance calculation of other nodes As we presented by the example of &amp;quot;mammal&amp;quot; and &amp;quot;elephant&amp;quot;, there are the cases where m one ontology a relatmnshlp m parent-child, but m the other ontology ~t m a grandparent-grandchild relaUonsh,p or a slbhng-relationship It would be better ff we took the charactenstms of each ontol- &amp;quot; ogy and differences of the ontologms into account m the calculatmn In particular, the reformation m ancestors might be very useful Other distance definitions In our method, we simply used the dice coefficmnt However, we can use more comphcated or sophmt,cared measures For example, (Resmk 1995) proposed a measure of semant,c similarity based on the notmn of information content Although thin proposal defines mmflanty between two nodes m a single taxonomy or ontology, we may be able to apply ,tm our mtuatmn (Aglrre et al 1995) proposed conceptual dmtance between nodes on ontologles captured by a Conceptual Density formula It is also a defimtmn m a single ontology Recently, (O'Hara and et al 1998) conducted an experiment of matchmg two ontologms, Wordconsider the characteristics of the ontologms One goal of our future ~ork is to understand how to incorporate such characteristics into these statmt,cal methods</Paragraph>
  </Section>
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