A strategy to estimate the optimal low-rank in incremental SVD-based algorithms for recommender systems

Recommender systems apply machine learning and data mining techniques for filtering unseen information, and they can provide an opportunity to predict whether a user would be interested in a given item. The main types of recommender systems are collaborative filtering (CF) and content-based filtering, which suffer from scalability and data sparsity resulting in poor quality recommendations and reduced coverage. There are two incremental algorithms based on Singular Value Decomposition (SVD) with high scalability for recommender systems which are named the incremental SVD algorithm and incremental Approximating the Singular Value Decomposition (ApproSVD) algorithm. In both mentioned methods, the estimated value of rank for approximating the recommender systems' data matrix is chosen experimentally in the related literature. In this paper, we investigate the role of singular values for estimating a more reliable amount of rank in the mentioned dimensionality reduction techniques to improve the recommender systems' performance. In other words, we offered a strategy for choosing the optimal rank that approximates the data matrix more accurately in incremental algorithms with the help of singular values. The numerical results illustrate that the suggested strategy improves the accuracy of the recommendations and run times of both algorithms when employs for Movielens, Netflix, and Jester dataset.