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<Paper uid="N06-2010">
  <Title>Gesture Improves Coreference Resolution</Title>
  <Section position="3" start_page="37" end_page="37" type="intro">
    <SectionTitle>
2 Implementation
</SectionTitle>
    <Paragraph position="0"> A set of commonly-used linguistic features were selected for this problem (Table 1). The first five features apply to pairs of NPs; the next set of features are applied individually to both of the NPs that are candidates for coreference. Thus, we include two features each, e.g., J is PRONOUN and I is PRONOUN, indicating respectively whether the candidate anaphor and candidate antecedent are pronouns. We include separate features for each of the four most common pronouns: &amp;quot;this&amp;quot;, &amp;quot;it&amp;quot;, &amp;quot;that&amp;quot;, and &amp;quot;they,&amp;quot; yielding features such as J=&amp;quot;this&amp;quot;.</Paragraph>
    <Section position="1" start_page="37" end_page="37" type="sub_section">
      <SectionTitle>
2.1 Gesture Features
</SectionTitle>
      <Paragraph position="0"> The gesture features shown in Table 1 are derived from the raw hand positions using a simple, deterministic system. Temporally, all features are computed at the midpoint of each candidate NP; for a further examination of the sensitivity to temporal offset, see (Eisenstein and Davis, 2006).</Paragraph>
      <Paragraph position="1"> At most one hand is determined to be the &amp;quot;focus hand,&amp;quot; according to the following heuristic: select the hand farthest from the body in the x-dimension, as long as the hand is not occluded and its y-position is not below the speaker's waist. If neither hand meets these criteria, than no hand is said to be in focus. Occluded hands are also not permitted to be in focus; the listener's perspective was very similar to that of the camera, so it seemed unlikely that the speaker would occlude a meaningful gesture. In addition, our system's estimates of the position of an occluded hand are unlikely to be accurate.</Paragraph>
      <Paragraph position="2"> If focus hands can be identified during both mentions, the Euclidean distance between focus points is computed.</Paragraph>
      <Paragraph position="3"> The distance is binned, using the supervised method described in (Fayyad and Irani, 1993). An advantage of binning the continuous features is that we can create a special bin for missing data, which occurs whenever a focus hand cannot be identified.</Paragraph>
      <Paragraph position="4"> If the same hand is in focus during both NPs, then the value of WHICH HAND is set to &amp;quot;same&amp;quot;; if a different hand is in focus then the value is set to &amp;quot;different&amp;quot;; if a focus hand cannot be identified in one or both NPs, then the value is set to &amp;quot;missing.&amp;quot; This multi-valued feature is automatically converted into a set of boolean features, so that all features can be represented as binary variables.</Paragraph>
    </Section>
    <Section position="2" start_page="37" end_page="37" type="sub_section">
      <SectionTitle>
2.2 Coreference Resolution Algorithm
</SectionTitle>
      <Paragraph position="0"> (McCallum and Wellner, 2004) formulates coreference resolution as a Conditional Random Field, where mentions are nodes, and their similarities are represented as weighted edges. Edge weights range from [?][?] to [?], with larger values indicating greater similarity. The optimal solution is obtained by partitioning the graph into cliques such that the sum of the weights on edges within cliques is maximized, and the sum of the weights on edges between cliques is minimized:</Paragraph>
      <Paragraph position="2"> In equation 1, x is a set of mentions and y is a coreference partitioning, such that yi,j = 1 if mentions xi and xj corefer, and yi,j = [?]1 otherwise. s(xi,xj) is a similarity score computed on mentions xi and xj.</Paragraph>
      <Paragraph position="3"> Computing the optimal partitioning ^y is equivalent to the problem of correlation clustering, which is known to be NP-hard (Demaine and Immorlica, to appear). Demaine and Immorlica (to appear) propose an approximation using integer programming, which we are currently investigating. However, in this research we use average-link clustering, which hierarchically groups the mentions x, and then forms clusters using a cutoff chosen to maximize the f-measure on the training set.</Paragraph>
      <Paragraph position="4"> We experiment with both pipeline and joint models for computing s(xi,xj). In the pipeline model, s(xi,xj) is the posterior of a classifier trained on pairs of mentions.</Paragraph>
      <Paragraph position="5"> The advantage of this approach is that any arbitrary classifier can be used; the downside is that minimizing the error on all pairs of mentions may not be equivalent to minimizing the overall error of the induced clustering. For experiments with the pipeline model, we found best results by boosting shallow decision trees, using the Weka implementation (Witten and Frank, 1999).</Paragraph>
      <Paragraph position="6"> Our joint model is based on McCallum and Wellner's (2004) adaptation of the voted perceptron to coreference resolution. Here, s is given by the product of a vector of weights l with a set of boolean features ph(xi,xj) induced from the pair of noun phrases: s(xi,xj) = lph(xi,xj). The maximum likelihood weights can be approximated by a voted perceptron, where, in the iteration t of the perceptron training:</Paragraph>
      <Paragraph position="8"> In equation 2, y[?] is the ground truth partitioning from the labeled data. ^y is the partitioning that maximizes equation 1 given the set of weights lt[?]1. As before, average-link clustering with an adaptive cutoff is used to partition the graph. The weights are then averaged across all iterations of the perceptron, as in (Collins, 2002).</Paragraph>
    </Section>
  </Section>
class="xml-element"></Paper>