# A Technique of Recursive Reliability-Based Missing Data Imputation for Collaborative Filtering
## 3 Related Studies  
In this section, we review related studies. We can roughly classify these studies into the following three categories: (1) studies that use the CF method in various fields; (2) studies that solve the data sparsity problem with EMDP method; and (3) studies that solve the data sparsity problem with AutAI and AdaM methods. Due to its simplicity and ease of implementation, the CF-based methods are used in a variety of recommendation systems to predict the interests of users. For example, [PERSON] et al. [4] proposed a CF approach for efficient movie recommendations using two similarity measures: item-item correlation and item-item adjusted cosine similarity. [PERSON] et al. [5] proposed a method that improves the efficiency of music recommendations by integrating data collected from the web into user ratings. [PERSON] et al. [6] proposed a personalized recommender system that considers users' activities, behaviors, and relationships between them in predicting Points of Interest (POIs) travel recommendations. [PERSON] et al. [7] also proposed integrating user's contextual information, i.e., opinion mining from textual reviews and posts, into personalized recommender systems to provide efficient recommendations to the tourists. Similar work was also performed by [PERSON] et al. [8; 9], where the authors proposed a product recommendation system that considers internal user factors, i.e., user sentimental deviations and the review's reliability. Recently, an artificial intelligence-based product recommendation approach, called Neural Interactive Collaborative Filtering, was proposed by [PERSON] et al. [10]. The authors used an efficient Q-learning mechanism to solve the cold-start and warm-start recommendation problems. [PERSON] et al. [11] proposed a personalized recommendation method for online video learning resources using an association rule mining mechanism to discover helpful videos for students. There were several methods to solve the data sparsity problem. For example, [PERSON] et al. [11] proposed an Effective Missing Data Prediction (EMDP) method, which prioritizes high reliability data for imputation and defines imputation data as data with similarity exceeding the threshold. Here, the similarity is computed using the equation proposed by [PERSON] [27], which is based on the modified Pearson's Correlation Coefficient. Considering that the Pearson's Correlation Coefficient determines similarity based on datasets of items rated by both users, its reliability decreases if the number of the rated items is small. Therefore, a higher weight is assigned to larger data size. That is, when the Pearson's Correlation Coefficient values are identical, the data with a larger intersection size is considered to have a higher similarity. In other words, by adding weight to the similarity measure in EMDP, we can lower the similarity value obtained from a dataset with a small number of items rated by both users. Equation (6) for user-user similarity computation is the result of adding this weight to Equation (1), where \(|I_{a}\cap I_{b}|\) is the number of items rated by both users. In the same manner, the item-item similarity is obtained by adding this weight to Equation (2), as expressed by Equation (7), where \(|U_{s}\cap U_{t}|\) is the number of users that rated both items. Here, parameters \(\gamma\) and \(\delta\) are input values for user similarity and item similarity, respectively, and the computed similarity value of an item rated by both users is defined to be reliable only when it is larger than or equal to \(\gamma\) and \(\delta\). Accordingly, when weight is assigned to \(Sim^{\prime}_{u}(a,\ b)\), the lower value between \(|I_{a}\cap I_{b}|\) and \(\gamma\) is taken as the numerator and is divided by the denominator \(\gamma\) to prevent \(Sim^{\prime}_{u}(a,\ b)\) from exceeding 1, as per the basic definition of similarity.