Ratings are frequently used to evaluate and compare subjects in various applications, from education to healthcare, because ratings provide succinct yet credible measures for comparing subjects. However, when multiple rating lists are combined or considered together, subjects often have missing ratings, because most rating lists do not rate every subject in the combined list. In this study, we propose analyses on missing value patterns using six real-world data sets in various applications, as well as the conditions for applicability of imputation algorithms. Based on the special structures and properties derived from the analyses, we propose optimization models and algorithms that minimize the total rating discordance across rating providers to impute missing ratings in the combined rating lists, using only the known rating information. The total rating discordance is defined as the sum of the pairwise discordance metric, which can be written as a quadratic function. Computational experiments based on real-world and synthetic rating data sets show that the proposed methods outperform the state-of-the-art general imputation methods in the literature in terms of imputation accuracy.

本研究在不同应用中使用六个真实数据集，分析缺失值模式以及插补算法的适用条件。基于分析得到的结构和属性，我们提出了优化模型和算法，在仅使用已知评分信息的情况下最小化评分提供者之间的总评分不一致性，用于插补组合评分列表中的缺失评分。实验结果表明，所提出的方法在插补准确性方面优于文献中的现有通用插补方法。

基于最小化不一致性的评分数据缺失值填充算法