On the mathematical relationship between expected n-call@k and the relevance vs. diversity trade-off

  • Authors:
  • Kar Wai Lim;Scott Sanner;Shengbo Guo

  • Affiliations:
  • ANU & NICTA, Canberra, Australia;NICTA & ANU, Canberra, Australia;Xerox Research Centre Europe, Grenoble, France

  • Venue:
  • SIGIR '12 Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

It has been previously noted that optimization of the n-call@k relevance objective (i.e., a set-based objective that is 1 if at least n documents in a set of k are relevant, otherwise 0) encourages more result set diversification for smaller n, but this statement has never been formally quantified. In this work, we explicitly derive the mathematical relationship between expected n-call@k and the relevance vs. diversity trade-off --- through fortuitous cancellations in the resulting combinatorial optimization, we show the trade-off is a simple and intuitive function of n (notably independent of the result set size k e n), where diversification increases as n approaches 1.