# A Technique of Recursive Reliability-Based Missing Data Imputation for Collaborative Filtering
###### Abstract  
Collaborative filtering (CF) is a recommendation technique that analyzes the behavior of various users and recommends the items preferred by users with similar preferences. However, CF methods suffer from poor recommendation accuracy when the user preference data used in the recommendation process is sparse. Data imputation can alleviate the data sparsity problem by substituting a virtual part of the missing user preferences. In this paper, we propose a k-recursive reliability-based imputation (k-RRI) that first selects data with high reliability and then recursively imputes data with additional selection while gradually lowering the reliability criterion. We also propose a new similarity measure that weights common interests and indifferences between users and items. The proposed method can overcome disregarding the importance of missing data and resolve the problem of poor data imputation of existing methods. The experimental results demonstrate that the proposed approach significantly improves recommendation accuracy compared to those resulting from the state-of-the-art methods while demanding less computational complexity. artificial intelligence; collaborative filtering; data sparsity; missing data imputation; recommendation systems; recursive algorithm; reliability +
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the original user-item interaction, we call it a pure CF method [3]. The pure CF method can only provide satisfactory recommendations for users, considering that there are sufficient past interactions. However, in actual systems, the user is often restricted in expressing preferences for items. In other words, the number of evaluations of items is much smaller than that of the actual number of items selected. As a result, the pure CF methods suffer from poor recommendation accuracy due to insufficient user preference data. We can refer to this problem as a data sparsity problem. Generally, the CF method is used in a variety of recommendation systems to predict the interests of users, including movie and music [4; 5], travel routes [6; 7], products [8; 9; 10], and online resources [11]. Various methods are proposed to solve the data sparsity problem in CF methods by substituting a virtual part of the nonexistent user preferences. For example, [PERSON] et al. [12] proposed an Effective Missing Data Prediction (EMDP) method, which prioritizes high-reliability data for imputation and only imputes the missing data when it exceeds the predefined threshold. Other methods [13; 14; 15; 16] incorporated the EMDP method into their proposed methods to solve a data sparsity problem in various fields. The main advantage of EMDP is that it can avoid poor imputation (no or insufficient amount of imputed data) because it imputes all the data whose similarities with the active user and active item exceed the thresholds. However, the main disadvantage of EMDP is a relatively poor accuracy because it gives the same value to all missing data [17]. On the other hand, [PERSON] et al. [18; 19; 20; 21] proposed the Auto-Adaptive Imputation (AutAI) and Adaptive Maximum imputation (AdaM) methods, which consider neighborhood information when imputing missing data. That is, AutAI and AdaM impute data of high importance by focusing on data rated by both users. Considering that the data imputed by AutAI and AdaM are highly important data containing most information on the prediction data, high accuracy can be maintained even with a small number of imputed missing data. However, the main limitation of these approaches is the risk of poor imputation, leading to no or insufficient imputed data in some cases, where the user's rating history is much smaller than those of other users [22; 23]. In this paper, we propose a k-recursive reliability-based imputation (k-RRI) for CF. The proposed method can overcome the disadvantage of EMDP of disregarding the importance of missing data and resolving the problem of poor data imputation of AutAI and AdaM.