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<?xml version="1.0" standalone="yes"?> <Paper uid="W99-0603"> <Title>Mapping Multilingual Hierarchies Using Relaxation Labeling</Title> <Section position="4" start_page="0" end_page="12" type="metho"> <SectionTitle> 2 Application of Relaxation Labeling to NLP </SectionTitle> <Paragraph position="0"> Relaxation labeling (RL) is a generic name for a family of iterative algorithms which perform function optimization, based on local information. See (Torras, 1989) for a summary. Its most remarkable feature is that it can deal with any kind of constraints, thus, the model can be improved by adding any constraints available, and the algorithm is independent of the complexity of the model. That is, we can use more sophisticated constraints without changing the algorithm.</Paragraph> <Paragraph position="1"> The algorithm has been applied to POS tagging (Mkrquez and Padrd, 1997), shallow parsing (Voutilainen and Padrd, 1997) and to word sense disambiguation (Padrd, 1998).</Paragraph> <Paragraph position="2"> Although ocher function optimization algorithms could have been used (e.g. genetic algorithms, simmulated annealing, etc.), we found RL to be suitable to our purposes, given its ability to use models based on context constraints, and the existence of previous work on applying it to NLP tasks.</Paragraph> <Paragraph position="3"> Detailed explanation of the algorithm can be found in (Torras, 1989), while its application to NLP tasks, advantages and drawbacks are addressed in (padrS, 1998).</Paragraph> <Section position="1" start_page="12" end_page="12" type="sub_section"> <SectionTitle> 2.1 Algorithm Description </SectionTitle> <Paragraph position="0"> The Relaxation Labeling algorithm deals with a set of variables (which may represent words, synsets, etc.), each of which may take one among several different labels (POS tags, senses, MaD entries, etc.). There is also a set of constraints which state compatibility or incompatibility of a combination of pairs variable-label. The aim of the algorithm is to find a weight assignment for each possible label for each variable, such that (a) the weights for the labels of the same variable add up to one, and (b) the weight assignation satisfies -to the maximum possible extent- the set of constraints.</Paragraph> <Paragraph position="1"> Summarizing, the algorithm performs constraint satisfaction to solve a consistent labeling problem. The followed steps are:</Paragraph> <Paragraph position="3"> Start with a random weight assignment.</Paragraph> <Paragraph position="4"> Compute the support value for each label of each variable. Support is computed according to the constraint set and to the current weights for labels belonging to context variables.</Paragraph> <Paragraph position="5"> .</Paragraph> <Paragraph position="6"> .</Paragraph> <Paragraph position="7"> Increase the weights of the labels more compatible with the context (larger support) and decrease those of the less compatible labels (smaller support). Weights are changed proportionally to the support received from the context.</Paragraph> <Paragraph position="8"> If a stopping/convergence criterion is satisfied, stop, otherwise go to step 2. We use the criterion of stopping when there are no more changes, although more sophisticated heuristic procedures may also be used to stop relaxation processes (Eklundh and Rosenfeld, 1978; Richards et al., 1981). The cost of the algorithm is proportional to the product of the number of variables by the number of constraints.</Paragraph> </Section> <Section position="2" start_page="12" end_page="12" type="sub_section"> <SectionTitle> 2.2 Application to taxonomy mapping </SectionTitle> <Paragraph position="0"> As described in previous sections, the problem we are dealing with is to map two taxonomies.</Paragraph> <Paragraph position="1"> That is: * The starting point is a sense disambiguated Spanish taxonomy-automatically extracted from a monolingual dictionary (Rigau et al., 1998)-.</Paragraph> <Paragraph position="2"> * We have a conceptual taxonomy (e.g.</Paragraph> <Paragraph position="3"> WordNet (Miller et al., 1991)), in which the nodes represent concepts, organized as synsets.</Paragraph> <Paragraph position="4"> * We want to relate both taxonomies in order to have an assignation of each sense of the Spanish taxonomy to a WN synset.</Paragraph> <Paragraph position="5"> The modeling of the problem is the following: * Each sense in the Spanish taxonomy is a variable for the relaxation algorithm.</Paragraph> <Paragraph position="6"> * The possible labels for that variable, are all the WN synsets which contain a word that is a possible translation of the Spanish sense. Thus, we will need a bilingual dictionary to know all the possible translations for a given Spanish word. This has the effect of losing the sense information we had in the Spanish taxonomy.</Paragraph> <Paragraph position="7"> * The algorithm will need constraints stating whether a synset is a suitable assignment for a sense. These constraints will rely on the taxonomy structure. Details are given in section 3.</Paragraph> </Section> </Section> <Section position="5" start_page="12" end_page="13" type="metho"> <SectionTitle> 3 The Constraints </SectionTitle> <Paragraph position="0"> Constraints are used by relaxation labeling algorithm to increase or decrease the weight for a variable label. In our case, constraints increase the weights for the connections between a sense in the Spanish taxonomy and a WordNet synset.</Paragraph> <Paragraph position="1"> Increasing the weight for a connection implies decreasing the weights for all the other possible connections for the same node. To increase the weight for a connection, constraints look for a.lready connected nodes that have the same relationships in both taxonomies.</Paragraph> <Paragraph position="2"> Although there is a wide range of relationships between WordNet synsets which can be used to build constraints, we have focused on the hyper/hyponym relationships. That is, we increase the weight for a connection when the involved nodes have hypernyms/hyponyms also connected. We consider hyper/hyponym relationships either directly or indirectly (i.e. ancestors or descendants), depending on the kind of constraint used.</Paragraph> <Paragraph position="3"> Figure 1 shows an example of possible connections between two taxonomies. Connection Ch will have its weight increased due to C5, C6 and C1, while connections C2 and Ca will have their weights decreased.</Paragraph> <Paragraph position="4"> o/\/ V\ --:: .......... ._o/2\o * I&quot;&quot;-. ..... :.-;.L-;L-L--:.. o/;\o Constraints are coded with three characters xYz, which are read as follows: The last character, z, indicates whether the constraints requires the existence of a connected hypernym (~), hyponym (o), or both (S). The two first characters indicate how the hyper/hyponym relationship is considered in the Spanish taxonomy (character x) and in WordNet (character Y=): (I) indicates that only immediate hyper/hyponym match, and (A) indicates that any ancestor/descendant matches.</Paragraph> <Paragraph position="5"> Thus, we have constraints IIE/nO which increase the weight for a connection between a Spanish sense and a WordNet synset when there is a connection between their respective hypernyms/hyponyms. Constraint Im requires the simultaneous satisfaction of IIE and II0.</Paragraph> <Paragraph position="6"> Similarly, we have constraints IAE/IAO, which increase the weight for a connection between a Spanish sense and a WordNet synset when there is a connection between the immediate hypernym/hyponym of the Spanish sense and any ancestor/descendant of the WN synset. Constraint IAB requires the simultaneous satisfaction of IAE and IAO. Symmetrically, constraints AtE, A10 and AIB, admit recursion on the Spanish taxonomy, but not in WordNet.</Paragraph> <Paragraph position="7"> Finally, constraints AAE, AAO and AAB, admit recursion on both sides.</Paragraph> <Paragraph position="8"> For instance, the following example shows a taxonomy in which the IIE constraint would be enough to connect the Spanish node rapaz to the <bird_of_prey> synset, given that there is a connection between ave (hypernym of rapaz) and animal <bird> (hypernym of Constraint lIE would -wrongly- connect the Spanish sense faisgn to the food <pheasant> synset, since there is a connection between its immediate hypernym (ave) and the immediate hypernym food <pheasant> (which is food <fowl,poultry,...>), but the animal synsets for ave are non-immediate ancestors of the animal synsets for <pheasant>. This would be rightly solved when using IAE or AAE constraints.</Paragraph> <Paragraph position="9"> More information on constraints and their application can be found in (Daud~ et al., 1999).</Paragraph> </Section> <Section position="6" start_page="13" end_page="14" type="metho"> <SectionTitle> 4 Experiments and Results </SectionTitle> <Paragraph position="0"> In this section we will describe a set of experiments and the results obtained. A brief description of the used resources is included to set the reader in the test environment.</Paragraph> <Section position="1" start_page="14" end_page="14" type="sub_section"> <SectionTitle> 4.1 Spanish Taxonomies </SectionTitle> <Paragraph position="0"> We tested the relaxation labeling algorithm with the described constraints on a set of disambiguated Spanish taxonomies automatically acquired from monolingual dictionaries. These taxonomies were automatically assigned to a WordNet semantic file (Rigau et al., 1997; Rigau et al., 1998). We tested the performance of the method on two different kinds of taxonomies: those assigned to a well defined and concrete semantic files (noun. animal, noun. food), and those assigned to more abstract and less structured ones (noun. cognition and noun. communication).</Paragraph> <Paragraph position="1"> We performed experiments directly on the taxonomies extracted by (Rigau et al., 1997), as well as on slight variations of them. Namely, we tested on the following modified taxonomies: +top Add a new virtual top as an hypernym of all the top nodes of taxonomies belonging to the same semantic file. The virtual top is connected to the top synset of the WordNet semantic file. In this way, all the taxonomies assigned to a semantic file, are * converted to a single one.</Paragraph> <Paragraph position="2"> no-senses The original taxonomies were built taking into account dictionary entries.</Paragraph> <Paragraph position="3"> Thus, the nodes are not words, but dictionary senses. This test consists of collapsing together all the sibling nodes that have the same word, regardless of the dictionary sense they came from. This is done as an attempt to minimize the noise introduced at the sense level by the taxonomy building procedure.</Paragraph> </Section> <Section position="2" start_page="14" end_page="14" type="sub_section"> <SectionTitle> 4.2 Bilingual dictionaries </SectionTitle> <Paragraph position="0"> The possible connections between a node in the Spanish taxonomy and WN synsets were extracted from bilingual dictionaries. Each node has as candidate connections all the synsets for all the words that are possible translations for the Spanish word, according to the bilingual dictionary. Although the Spanish taxonomy nodes are dictionary senses, bilingual dictionaries translate words. Thus, this step introduces noise in the form of irrelevant connections, since not all translations necessarily hold for a single dictionary sense.</Paragraph> <Paragraph position="1"> We used an integration of several bilingual sources availabl'e. This multi-source dictionary contains 124,949 translations (between 53,830 English and 41,273 Spanish nouns).</Paragraph> <Paragraph position="2"> Since not all words in the taxonomy appear in our bilingual dictionaries, coverage will be partial. Table 1 shows the percentage of nodes in each taxonomy that appear in the dictionaries (and thus, that may be connected to WN).</Paragraph> <Paragraph position="3"> Among the words that appear in the bilingual dictionary, some have only one candidate connection -i.e. are monosemous-. Since selecting a connection for these cases is trivial, we will focus on the polysemic nodes. Table 2 shows the percentage of polysemic nodes (over the number of words with bilingual connection) in each test taxonomy. The average polysemy ratio (number of candidate connections per Spanish sense) is 15.8, ranging from 9.7 for taxonomies in noun. animal, to 20.1 for less structured domains such as noun. communication.</Paragraph> </Section> <Section position="3" start_page="14" end_page="14" type="sub_section"> <SectionTitle> 4.3 Results </SectionTitle> <Paragraph position="0"> In the performed tests we used simultaneously all constraints with the same recursion pattern.</Paragraph> <Paragraph position="1"> This yields the packs: II*, AI*, IA* and AA*, which were applied to all the taxonomies for the four test semantic files.</Paragraph> <Paragraph position="2"> Table 3 presents coverage figures for the different test sets, computed as the amount of nodes for which some constraint is applied and thus their weight assignment is changed. Percentage is given over the total amount of nodes with bilingual connections.</Paragraph> <Paragraph position="3"> To evaluate the precision of the algorithm, we hand checked the results for the original taxonomies, using AA* constraints. Precision results can be divided in several cases, depending on the correctness of the Spanish taxonomies used as a starting point.</Paragraph> <Paragraph position="4"> ToK, Foh&quot; The Spanish taxonomy was well built and correctly assigned to the semantic file.</Paragraph> <Paragraph position="5"> ToK,FNoI~&quot; The Spanish taxonomy was well built, but wrongly assigned to the semantic file.</Paragraph> <Paragraph position="6"> TNOI( The Spanish taxonomy was wrongly built.</Paragraph> <Paragraph position="7"> In each case, the algorithm selects a conne('tion for each sense, we will count how many connections are right/wrong in the first and s~,cond cases. In the third case the taxonomy wa.~ wrongly extracted and is nonsense, so the assignations cannot be evaluated.</Paragraph> <Paragraph position="8"> Note that we can distinguish right/wrong assignations in the second case because the connections are taken into account over the whole WN, not only on the semantic file being processed. So, the algorithm may end up correctly assigning the words of a hierarchy, even when it was assigned to the wrong semantic file. For instance, in the hierarchy piel (skin, Fur, peel, pelt) ==~marta (sable, marten, coal_back) ==~.vison (mink, mink_coat) all words may belong either to the semantic file noun. substance (senses related to fur, pelt) or to noun.animal (animal, animal_part senses), among others. The right noun.substance synsets for each word are selected, since there was no synset for piel that was ancestor of the animal senses of marta and visdn.</Paragraph> <Paragraph position="9"> In this case, the hierarchy was well built, and well solved by the algorithm. The only mistake was having assigned it to the noun.animal semantic file, so we will count it as a right choice of the relaxation labeling algorithm, but write it in a separate column.</Paragraph> <Paragraph position="10"> Tables 4 and 5 show the precision rates for each original taxonomy. In the former, figures are given over polysemic words (nodes with more than one candidate connection). In the later, figures are computed overall (nodes with at least one candidate connection).</Paragraph> <Paragraph position="11"> Accuracy is computed at the semantic file level, i.e., if a word is assigned a synset of the right semantic file, it is computed as right, otherwise, as wrong.</Paragraph> <Paragraph position="12"> To give an idea of the task complexity and the quality of the reported results, even with this simplified evaluation, consider the following: * Those nodes with only one possible synset for the right semantic file (30% in average, ranging from 22% in noun. communication to 45% in noun.animal) are not affected by the evaluation at the semantic file level. * The remaining nodes have more than one possible synset in the right semantic file: 6.3 in average (ranging from 3.0 for noun.animal to 8.7 for noun. communication).</Paragraph> <Paragraph position="13"> * Thus, we can consider that we are evaluating a task easier than the actual one (the actual evaluation would be performed at the synset level). This simplified task has an average polysemy of 6.7 possible choices per sense, while the actual task at the synset level would have 15.8. Although this situates the baseline of a random assignment about 15% instead of 6%, it is still a hard task.</Paragraph> </Section> </Section> <Section position="7" start_page="14" end_page="14" type="metho"> <SectionTitle> 5 Conclusions </SectionTitle> <Paragraph position="0"> We have applied the relaxation labeling algorithm to assign an appropriate WN synset to each node of an automatically extracted taxonomy. Results for two different kinds of conceptual structures have been reported, and they point that this may be an accurate and robust method (not based on ad-hoc heuristics) to connect hierarchies (even in different languages).</Paragraph> <Paragraph position="1"> The experiments performed up to now seem to indicate that: * The relaxation labeling algorithm is a good technique to link two different hierarchies.</Paragraph> <Paragraph position="2"> For each node with several possible connections, the candidate that best matches the surrounding structure is selected.</Paragraph> <Paragraph position="3"> * The only information used by the algorithm are the hyper/hyponymy relationships in both taxonomies. These local constraints are propagated throughout the hierarchies to produce a global solution.</Paragraph> <Paragraph position="4"> * There is a certain amount of noise in the different phases of the process. First, the taxonomies were automatically acquired and assigned to semantic files. Second, the bilingual dictionary translates words, not senses, which introduces irrelevant candidate connections.</Paragraph> <Paragraph position="5"> * The size and coverage of the bilingual dictionaries used to establish the candidate connections is an important issue. A dictionary with larger coverage increases the amount of nodes with candidate connections and thus the algorithm coverage</Paragraph> </Section> <Section position="8" start_page="14" end_page="17" type="metho"> <SectionTitle> 6 Proposals for Further Work </SectionTitle> <Paragraph position="0"> Some issues to be addressed to improve the algorithm performance are the following: * Further test and evaluate the precision of the algorithm. In this direction we plan -apart from performing wider hand checking of the results, both to file and synset level- to use the presented technique to link WN1.5 with WN1.6. Since there is already a mapping between both versions, the experiment would provide an idea of the accuracy of the technique and of its applicability to different hierarchies of the same language. In addition, it would constitute an easy way to update existing lexical resources. null * Use other relationships apart from hyper/hyponymy to build constraints to select the best connection (e.g. sibling.</Paragraph> <Paragraph position="1"> cousin, synonymy, meronymy, etc.).</Paragraph> <Paragraph position="2"> * To palliate the low coverage of the bilingual dictionaries, candidate translations could be inferred from connections of surrounding senses. For instance, if a sense has no candidate connections, but its hypernym does, we could consider as candidate connections for that node all the hyponyms of the synset connected to its hypernym.</Paragraph> <Paragraph position="3"> * Use the algorithm to enrich the Spanish part of EuroWordNet taxonomy. It could also be applied to include taxonomies for other languages not currently in the SWN project.</Paragraph> <Paragraph position="4"> In addition, some ideas to further exploit the possibilities of these techniques are: * Use EWN instead of WN as the target taxonomy. This would largely increase the coverage, since the candidate connections missing in the bilingual dictionaries could be obtained from the Spanish part of EWN, and viceversa. In addition, it would be usetiff to detect gaps in the Spanish part of EWN, since a EWN synset with no Spanish words in EWN, could be assigned one via the connections obtained from the bilingual dictionaries.</Paragraph> <Paragraph position="5"> * Since we are connecting dictionary senses (the entries in the MRD used to build the taxonomies) to EWN synsets: First of all, we could use this to disambiguate the right sense for the genus of an entry. For instance, in the Spanish taxonomies, the genus for the entry queso_l (cheese) is masa (mass) but this word has several dictionary entries. Connecting the taxonomy to EWN, we would be able to find out which is the appropriate sense for m~sa, and thusl which is the right genus sense for queso_l. Secondly, once we had each dictionary sense connected to a EWN synset, we could enrich EWN with the definitions in the MaD, using them as Spanish glosses.</Paragraph> <Paragraph position="6"> * Map the Spanish part of EWN to WN1.6.</Paragraph> <Paragraph position="7"> This could be done either directly, or via mapping WN 1.5-WN 1.6.</Paragraph> </Section> class="xml-element"></Paper>