<?xml version="1.0" standalone="yes"?>
<Paper uid="W06-3815">
  <Title>Context Comparison as a Minimum Cost Flow Problem</Title>
  <Section position="2" start_page="0" end_page="97" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Many natural language problems can be cast as a problem of comparing &amp;quot;contexts&amp;quot; (units of text). For example, the local context of a word can be used to resolve its ambiguity (e.g., Sch&amp;quot;utze, 1998), assuming that words used in similar contexts are closely related semantically (Miller and Charles, 1991). Extending the meaning of context, the content of a document may reveal which document class(es) it belongs to (e.g., Xu et al., 2003). In any application, once a sensible view of context is formulated, the next step is to choose a representation that makes comparisons possible. For example, in word sense disambiguation, a context of an ambiguous instance can be represented as a vector of the frequencies of words surrounding it. Until recently, the dominant approach has been a non-graphical one-context comparison is reduced to a task of measuring distributional distance between context vectors. The difference in the frequency characteristics of contexts is used as an indicator of the semantic distance between them.</Paragraph>
    <Paragraph position="1"> We present a graphical alternative that combines both distributional and ontological knowledge. We begin with the use of a different context representation that allows easy incorporation of ontological information. Treating an ontology as a network, we can represent a context as a set of nodes in the network (i.e., concepts in the ontology), each with a weight (i.e., frequency). To contrast our work with that of Navigli and Velardi (2005) and Mihalcea (2006), the goal is not merely to provide a graphical representation for a context in which the relevant concepts are connected. Rather, contexts are treated as weighted subgraphs within a larger graph in which they are connected via a set of paths. By incorporating the semantic distance between individual concepts, the graph (representing the ontology) becomes a metric space in which we can measure the distance between subgraphs (representing the contexts to be compared).</Paragraph>
    <Paragraph position="2"> More specifically, measuring the distance between two contexts can be viewed as solving a minimum cost flow (MCF) problem by calculating the amount of &amp;quot;effort&amp;quot; required for transporting the flow from one context to the other. Our method has the advantage of including semantic information (by making use of the graphical structure of an ontology) without losing distributional information (by  using the concept frequencies derived from corpus data).</Paragraph>
    <Paragraph position="3"> This network flow formulation, though supporting the inclusion of an ontology in context comparison, is not flexible enough. The problem is rooted in the choice of concept-to-concept distance (i.e., the distance between two concepts, to contrast it from the overall semantic distance between two contexts).</Paragraph>
    <Paragraph position="4"> Certain concept-to-concept distances may result in a difficult-to-process network which severely compromises efficiency. To remedy this, we propose a novel network transformation method for constructing a pared-down network which mimics the structure of the more precise network, but without the expensive processing or any significant information loss as a result of the transformation.</Paragraph>
    <Paragraph position="5"> In the remainder of this paper, we first present the underlying network flow framework, and develop a more efficient variant of it. We then evaluate the robustness of our methods on a context comparison task. Finally, we conclude with an analysis and some future directions.</Paragraph>
  </Section>
class="xml-element"></Paper>