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A quadratic lower bound for Rocchio’s similarity-based relevance feedback algorithm with a fixed query updating factor

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Listed:
  • Zhixiang Chen

    (University of Texas-Pan American)

  • Bin Fu

    (University of Texas-Pan American)

  • John Abraham

    (University of Texas-Pan American)

Abstract

Rocchio’s similarity-based relevance feedback algorithm, one of the most important query reformation methods in information retrieval, is essentially an adaptive supervised learning algorithm from examples. In practice, Rocchio’s algorithm often uses a fixed query updating factor. When this is the case, we strengthen the linear Ω(n) lower bound obtained by Chen and Zhu (Inf. Retr. 5:61–86, 2002) and prove that Rocchio’s algorithm makes Ω(k(n−k)) mistakes in searching for a collection of documents represented by a monotone disjunction of k relevant features over the n-dimensional binary vector space {0,1} n , when the inner product similarity measure is used. A quadratic lower bound is obtained when k is linearly proportional to n. We also prove an O(k(n−k)3) upper bound for Rocchio’s algorithm with the inner product similarity measure in searching for such a collection of documents with a constant query updating factor and a zero classification threshold.

Suggested Citation

  • Zhixiang Chen & Bin Fu & John Abraham, 2010. "A quadratic lower bound for Rocchio’s similarity-based relevance feedback algorithm with a fixed query updating factor," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 134-157, February.
    • Handle: RePEc:spr:jcomop:v:19:y:2010:i:2:d:10.1007_s10878-008-9169-6
    DOI: 10.1007/s10878-008-9169-6
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    References listed on IDEAS

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    1. Zhixiang Chen & Xiannong Meng & Richard H. Fowler & Binhai Zhu, 2001. "FEATURES: Real‐time adaptive feature and document learning for web search," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 52(8), pages 655-665.
    2. Zhixiang Chen & Bin Fu, 2007. "On the complexity of Rocchio's similarity‐based relevance feedback algorithm," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(10), pages 1392-1400, August.
    3. Vijay V. Raghavan & S. K. M. Wong, 1986. "A critical analysis of vector space model for information retrieval," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 37(5), pages 279-287, September.
    4. Gerard Salton & Chris Buckley, 1990. "Improving retrieval performance by relevance feedback," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 41(4), pages 288-297, June.
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