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<Paper uid="P06-1033">
  <Title>Graph Transformations in Data-Driven Dependency Parsing</Title>
  <Section position="5" start_page="258" end_page="258" type="metho">
    <SectionTitle>
LIBSVM (Chang and Lin, 2005).
2.5 Related Work
</SectionTitle>
    <Paragraph position="0"> Other ways of improving parsing accuracy with respect to coordination include learning patterns of morphological and semantical information for the conjuncts (Park and Cho, 2000). More specifically for PDT, Collins et al. (1999) relabel coordinated phrases after converting dependency structures to phrase structures, and Zeman (2004) uses a kind of pattern matching, based on frequencies of the parts-of-speech of conjuncts and conjunctions. Zeman also mentions experiments to transform the dependency structure for coordination but does not present any results.</Paragraph>
    <Paragraph position="1"> Graph transformations in dependency parsing have also been used in order to recover non-projective dependencies together with parsers that are restricted to projective dependency graphs.</Paragraph>
    <Paragraph position="2"> Thus, Nivre and Nilsson (2005) improve parsing accuracy for MaltParser by projectivizing training data and applying an inverse transformation to the output of the parser, while Hall and Nov'ak (2005) apply post-processing to the output of Charniak's parser (Charniak, 2000). In the final experiments below, we combine these techniques with the transformations investigated in this paper.</Paragraph>
  </Section>
  <Section position="6" start_page="258" end_page="260" type="metho">
    <SectionTitle>
3 Dependency Graph Transformations
</SectionTitle>
    <Paragraph position="0"> In this section, we describe algorithms for transforming dependency graphs in PDT from PS to MS and back, starting with coordination and continuing with verb groups.</Paragraph>
    <Section position="1" start_page="258" end_page="260" type="sub_section">
      <SectionTitle>
3.1 Coordination
</SectionTitle>
      <Paragraph position="0"> The PS-to-MS transformation for coordination will be designated tc([?]), where [?] is a data set.</Paragraph>
      <Paragraph position="1"> The transformation begins with the identification of a base conjunction, based on its dependency type (Coord) and/or its part-of-speech (J^). For example, the word a (and) in figure 1 is identified as a base conjunction.</Paragraph>
      <Paragraph position="2">  Before the actual transformation, the base conjunction and all its dependents need to be classified into three different categories. First, the base conjunction is categorized as a separator (S). If the coordination consists of more than two conjuncts, it normally has one or more commas separating conjuncts, in addition to the base conjunction. These are identified by looking at their dependency type (mostly AuxX) and are also categorized as S. The coordination in figure 1 contains no commas, so only the word a will belong to S.</Paragraph>
      <Paragraph position="3"> The remaining dependents of the base conjunction need to be divided into conjuncts (C) and other dependents (D). To make this distinction, the algorithm again looks at the dependency type.</Paragraph>
      <Paragraph position="4"> In principle, the dependency type of a conjunct has the suffix Co, although special care has to be taken for coordinated prepositional cases and embedded clauses (B&amp;quot;ohmov'a et al., 2003). The words bojovnost'i and tvrdost'i in figure 1, both having the dependency type Obj Co, belong to the category C. Since there are no other dependents of a, the coordination contains no instances of the category D.</Paragraph>
      <Paragraph position="5"> Given this classification of the words involved in a coordination, the transformation tc([?]) is straightforward and basically connects all the arcs in a chain. Let C1,...,Cn be the elements of C, ordered by linear precedence, and let S1i,...,Smi be the separators occurring between Ci and Ci+1.</Paragraph>
      <Paragraph position="6"> Then every Ci becomes the head of S1i,...,Smi, Smi becomes the head of Ci+1, and C1 becomes the only dependent of the original head of the base conjunction. The dependency types of the conjuncts are truncated by removing the suffix Co.2 Also, each word in wd [?] D becomes a dependent of the conjunct closest to its left, and if such a word does not exist, wd will depend on the leftmost conjunct. After the transformation tc([?]), every coordination forms a left-headed chain, as illustrated in figure 2.</Paragraph>
      <Paragraph position="7"> This new representation creates a problem, however. It is no longer possible to distinguish the dependents in D from other dependents of the conjuncts. For example, the word Velkou in figure 2 is not distinguishable from a possible dependent in D, which is an obvious drawback when transforming back to PS. One way of distinguishing D elements is to extend the set of dependency types.</Paragraph>
      <Paragraph position="8"> 2Preliminary results indicated that this increases parsing accuracy.</Paragraph>
      <Paragraph position="9"> The dependency type r of each wd [?] D can be replaced by a completely new dependency type r+ (e.g., Atr+), theoretically increasing the number of dependency types to 2* |R|.</Paragraph>
      <Paragraph position="10"> The inverse transformation, t[?]1c ([?]), again starts by identifying base conjunctions, using the same conditions as before. For each identified base conjunction, it calls a procedure that performs the inverse transformation by traversing the chain of conjuncts and separators &amp;quot;upwards&amp;quot; (right-to-left), collecting conjuncts (C), separators (S) and potential conjunction dependents (Dpot).</Paragraph>
      <Paragraph position="11"> When this is done, the former head of the left-most conjunct (C1) becomes the head of the right-most (base) conjunction (Smn[?]1). In figure 2, the leftmost conjunct is bojovnost'i, with the head vyznaVcovalo, and the rightmost (and only) conjunction is a, which will then have vyznaVcovalo as its new head. All conjuncts in the chain become dependents of the rightmost conjunction, which means that the structure is converted back to the one depicted in figure 1.</Paragraph>
      <Paragraph position="12"> As mentioned above, the original structure in figure 1 did not have any coordination dependents, but Velkou [?] Dpot. The last step of the inverse transformation is therefore to sort out conjunction dependents from conjunct dependents, where the former will attach to the base conjunction. Four versions have been implemented, two of which take into account the fact that the dependency types AuxG, AuxX, AuxY, and Pred are the only dependency types that are more frequent as conjunction dependents (D) than as conjunct dependents in the training data set:  elements in tc. Attach all words with label r+ to the base conjunction (and change the label to r) in t[?]1c .</Paragraph>
      <Paragraph position="13"> * tc+[?]: Extend arc labels from r to r+ for D elements in tc, except for the labels AuxG, AuxX, AuxY and Pred. Attach all words with label r+, AuxG, AuxX, AuxY, or Pred to the base conjunction (and change the label to r if necessary) in t[?]1c .</Paragraph>
    </Section>
    <Section position="2" start_page="260" end_page="260" type="sub_section">
      <SectionTitle>
3.2 Verb Groups
</SectionTitle>
      <Paragraph position="0"> To transform verb groups from PS to MS, the transformation algorithm, tv([?]), starts by identifying all auxiliary verbs in a sentence. These will belong to the set A and are processed from left to right. A word waux [?] A iff wmain AuxV[?]- waux, where wmain is the main verb. The transformation into MS reverses the relation between the verbs, i.e., waux AuxV[?]- wmain, and the former head of wmain becomes the new head of waux. The main verb can be located on either side of the auxiliary verb and can have other dependents (whereas auxiliary verbs never have dependents), which means that dependency relations to other dependents of wmain may become non-projective through the transformation. To avoid this, all dependents to the left of the rightmost verb will depend on the leftmost verb, whereas the others will depend on the rightmost verb.</Paragraph>
      <Paragraph position="1"> Performing the inverse transformation for verb groups, t[?]1v ([?]), is quite simple and essentially the same procedure inverted. Each sentence is traversed from right to left looking for arcs of the type waux AuxV[?]- wmain. For every such arc, the head of waux will be the new head of wmain, and wmain the new head of waux. Furthermore, since waux does not have dependents in PS, all dependents of waux in MS will become dependents of wmain in PS.</Paragraph>
    </Section>
  </Section>
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