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<Paper uid="W06-0108">
  <Title>Sydney, July 2006. c(c)2006 Association for Computational Linguistics Cluster-based Language Model for Sentence Retrieval in Chinese Question Answering</Title>
  <Section position="4" start_page="58" end_page="59" type="metho">
    <SectionTitle>
3 Cluster-based Language Model for
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="58" end_page="58" type="sub_section">
      <SectionTitle>
Sentence Retrieval
</SectionTitle>
      <Paragraph position="0"> Note that document model p(w|D) in document retrieval is replace by p(w|S) called sentence model in sentence retrieval.</Paragraph>
      <Paragraph position="1"> The assumption of cluster-based language model for retrieval is that topic-related sentences tend to be relevant to the same query. So, incorporating the topic of sentences into language model can improve the performance of sentence retrieval based on standard language model.</Paragraph>
      <Paragraph position="2"> The proposed cluster-based language model is a mixture model of three components, that are sentence model p  In fact, the cluster-based language model can also be viewed as a two-stage smoothing approach. The cluster model is first smoothed using the collection model, and the sentence model is then smoothed with the smoothed cluster model. In this paper, the cluster model is in the form of term distribution over cluster/topic, associated with the distribution of clusters/topics over sentence, which can be expressed by equation (4).</Paragraph>
      <Paragraph position="4"> where, T is the set of clusters/topics. p_topic(w|T) is cluster model. p(t|S) is topic sentence distribution which means the distribution of topic over sentence. And p(w|t) is term topic distribution which means the term distribution over topics.</Paragraph>
      <Paragraph position="5"> Before estimating the sentence model p(w|S), topic-related sentences should be organized into clusters/topics to estimate p(t|S) and p(w|t) probabilities. For sentence clustering, this paper presents two novel approaches that are One-Sentence-Multi-Topics and One-Sentence-One-Topic respectively.</Paragraph>
    </Section>
    <Section position="2" start_page="58" end_page="58" type="sub_section">
      <SectionTitle>
3.1 One-Sentence-Multi-Topics
</SectionTitle>
      <Paragraph position="0"> The main idea of One-Sentence-Multi-Topics can be summarized as follows.</Paragraph>
      <Paragraph position="1">  1. If a sentence includes M different candidate  answers, then the sentence consists of M different topics.</Paragraph>
      <Paragraph position="2"> For example, the sentence S5 in Table 1 includes two topics which are &amp;quot;Bei Er Fa Ming Dian Hua /Bell invented telephone&amp;quot; and &amp;quot;Ai Di Sheng Fa Ming Dian Deng /Edison invented electric light&amp;quot; respectively. 2. Different sentences have the same topic if two candidate answers are same.</Paragraph>
      <Paragraph position="3"> For example, the sentence S4 and S5 in Table 1 have the same topic &amp;quot;Bei Er Fa Ming Dian Hua /Bell invented telephone&amp;quot; because both of sentences have the same candidate answer &amp;quot;Bei Er /Bell&amp;quot;. Based on the above ideas, the result of sentence clustering based on One-Sentence-Multi-Topics is shown in Table 2.</Paragraph>
    </Section>
    <Section position="3" start_page="58" end_page="58" type="sub_section">
      <SectionTitle>
Topics Sentence Clustering
</SectionTitle>
      <Paragraph position="0"> So, we could estimate term topic distribution using equation (5).</Paragraph>
      <Paragraph position="2"> means the Kullback-Leibler divergence between the sentence with the cluster/topic. k denotes the number of cluster/topic. The main idea of equation (6) is that the closer the Kullback-Leibler divergence, the larger the topic sentence probability p(t|S).</Paragraph>
    </Section>
    <Section position="4" start_page="58" end_page="59" type="sub_section">
      <SectionTitle>
3.2 One-Sentence-One-Topic
</SectionTitle>
      <Paragraph position="0"> The main idea of One-Sentence-One-Topic also could be summarized as follows.</Paragraph>
      <Paragraph position="1">  1. A sentence only has one kernel candidate an null swer which represents the kernel topic no matter how many candidate answers is included. For example, the kernel topic of sentence S5 in Table 1 is &amp;quot;Bei Er Fa Ming Dian Hua /Bell invented telephone&amp;quot; though it includes three different candi- null date answers.</Paragraph>
      <Paragraph position="2"> 2. Different sentences have the same topic if two kernel candidate answers are same.</Paragraph>
      <Paragraph position="3"> For example, the sentence S4 and S5 in Table 1 have the same topic &amp;quot;Bei Er Fa Ming Dian Hua /Bell invented telephone&amp;quot;.</Paragraph>
      <Paragraph position="4"> 3. The kernel candidate answer has shortest average distance to all query terms.</Paragraph>
      <Paragraph position="5">  Based on the above ideas, the result of sentence clustering based on One-Sentence-One-Topic is shown in Table 3.</Paragraph>
    </Section>
    <Section position="5" start_page="59" end_page="59" type="sub_section">
      <SectionTitle>
Sentence Clustering
</SectionTitle>
      <Paragraph position="0"> Equation (8) and (9) can be used to estimate the kernel candidate answer and the distances of candidate answers respectively. Term topic distribution in One-Sentence-One-Topic can be estimated via equation (5). And topic sentence distribution is equal to 1 because a sentence only belongs to one cluster/topic.</Paragraph>
      <Paragraph position="2"/>
      <Paragraph position="4"/>
    </Section>
  </Section>
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