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In this study, our focus lies in the advancement of rapid algorithms for determining statistical rankings and user recommendation within highly incomplete and imbalanced data sets. Based on the HodgeRank algorithm, we describe the ranking problem on graphs. This allows us to formulate a least squares problem on graphs that gauges the reliability of the computed rankings. Given the escalating complexity of computations, as data set dimensions amplify, our research is driven by the need for pragmatic solutions that accommodate the efficient and precise computation of rankings. Specifically, we group elements based on their tier in a naive ranking and run the HodgeRank algorithm on smaller subgroups, which makes the method faster while maintaining the integrity of the ranking. We examine the efficacy and the time complexity of the proposed algorithm on the IMDb movie data set and systematically explore the impact of varying group sizes on algorithmic performance. With the proposed grouping method, we are able to reduce the complexity of the algorithm from \(O(n^3)\) to \(O(n^3/k^2)\) , where k is the group size while safeguarding the ranking accuracy. Using the algebraic multigrid preconditioner for computation in each subgroup, we are able to reduce the run time significantly.

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Faster HodgeRank Approximation Algorithm for Statistical Ranking and User Recommendation Problems

  • 章节

  • 发表日期：

    2025年

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  • Shelby Ferrier,
  • Junyuan Lin,
  • Guangpeng Ren

摘要

In this study, our focus lies in the advancement of rapid algorithms for determining statistical rankings and user recommendation within highly incomplete and imbalanced data sets. Based on the HodgeRank algorithm, we describe the ranking problem on graphs. This allows us to formulate a least squares problem on graphs that gauges the reliability of the computed rankings. Given the escalating complexity of computations, as data set dimensions amplify, our research is driven by the need for pragmatic solutions that accommodate the efficient and precise computation of rankings. Specifically, we group elements based on their tier in a naive ranking and run the HodgeRank algorithm on smaller subgroups, which makes the method faster while maintaining the integrity of the ranking. We examine the efficacy and the time complexity of the proposed algorithm on the IMDb movie data set and systematically explore the impact of varying group sizes on algorithmic performance. With the proposed grouping method, we are able to reduce the complexity of the algorithm from \(O(n^3)\) to \(O(n^3/k^2)\) , where k is the group size while safeguarding the ranking accuracy. Using the algebraic multigrid preconditioner for computation in each subgroup, we are able to reduce the run time significantly.