Discordance Minimization-based Imputation Algorithms for Missing Values in Rating Data

TL;DR

This paper introduces novel imputation algorithms that minimize rating discordance to accurately fill missing values in combined rating datasets, outperforming existing methods.

Contribution

It develops optimization models based on rating discordance minimization, tailored for specific data structures, and demonstrates superior imputation accuracy over current methods.

Findings

Proposed algorithms outperform state-of-the-art imputation methods.

Algorithms effectively handle various real-world missing data patterns.

Imputation accuracy is validated through experiments on real and synthetic datasets.

Abstract

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.