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<Paper uid="N06-2007">
  <Title>Semi-supervised Relation Extraction with Label Propagation</Title>
  <Section position="3" start_page="0" end_page="25" type="metho">
    <SectionTitle>
2 The Proposed Method
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="25" type="sub_section">
      <SectionTitle>
2.1 Problem Definition
</SectionTitle>
      <Paragraph position="0"> Let X = {xi}ni=1 be a set of contexts of occurrences of all entity pairs, where xi represents the contexts of the i-th occurrence, and n is the total number of occurrences of all entity pairs. The first l examples are labeled as yg ( yg [?]{rj}Rj=1, rj denotes relation type and R is the total number of relation types).</Paragraph>
      <Paragraph position="1"> And the remaining u(u = n[?]l) examples are unlabeled. null Intuitively, if two occurrences of entity pairs have  the similar contexts, they tend to hold the same relation type. Based on this assumption, we create a graph where the vertices are all the occurrences of entity pairs, both labeled and unlabeled. The edge between vertices represents their similarity. Then the task of relation extraction can be formulated as a form of propagation on a graph, where a vertex's label propagates to neighboring vertices according to their proximity. Here, the graph is connected with the weights: Wij = exp([?]s  ij a2 ), where sij is the sim-ilarity between x i and xj calculated by some similarity measures. In this paper,two similarity measures are investigated, i.e. Cosine similarity measure and Jensen-Shannon (JS) divergence (Lin, 1991). And we set a as the average similarity between labeled examples from different classes.</Paragraph>
    </Section>
    <Section position="2" start_page="25" end_page="25" type="sub_section">
      <SectionTitle>
2.2 Label Propagation Algorithm
</SectionTitle>
      <Paragraph position="0"> Given such a graph with labeled and unlabeled vertices, we investigate the label propagation algorithm (Zhu and Ghahramani, 2002) to help us propagate the label information of any vertex in the graph to nearby vertices through weighted edges until a global stable stage is achieved.</Paragraph>
      <Paragraph position="1"> Define a n x n probabilistic transition matrix T</Paragraph>
      <Paragraph position="3"> , where Tij is the probability to jump from vertex xj to vertex xi. Also define a nxR label matrix Y , where Yij representing the probabilities of vertex yi to have the label rj. Then the label propagation algorithm consists the following main steps: Step1: Initialization Firstly, set the iteration index t = 0. Then let Y 0 be the initial soft labels attached to each vertex and Y 0L be the top l rows of Y 0, which is consistent with the labeling in labeled data (Y 0ij = 1 if yi is label rj and 0 otherwise ). Let Y 0U be the remaining u rows corresponding to unlabeled data points and its initialization can be arbitrary.</Paragraph>
      <Paragraph position="4"> Step 2: Propagate the label by Y t+1 = TY t, where T is the row-normalized matrix of T, i.e.</Paragraph>
      <Paragraph position="5"> Tij = Tij/summationtextk Tik, which can maintain the class probability interpretation.</Paragraph>
      <Paragraph position="6"> Step 3: Clamp the labeled data, i.e., replace the top l row of Y t+1 with Y 0L. In this step, the labeled data is clamped to replenish the label sources from these labeled data. Thus the labeled data act like sources to push out labels through unlabeled data.</Paragraph>
    </Section>
  </Section>
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