A new algorithm for solving data sparsity problem based-on Non negative matrix factorization in recommender systems

The “sparsity” challenge is a well-known problem in recommender systems. This issue relates to little information about each user or item in large data set. The purpose of this paper is pre-processing of data and using Non negative Matrix Factorization (NMF) method to improve this challenge. Since the original data are non negative, the algorithm based on NMF maintains positive effect of data on decomposition matrices and makes better prediction of original data in comparison to singular value decomposition (SVD) algorithm. Since the dimensions of data are very large, it offers a solution based on dimensionality reduction in which useful factors for selecting optimal dimensions (optimal `k') are extracted from the data matrix until appropriate approximation of the original data obtains from rank `k' matrices. Thus, the presented model not only selects the best factors from the original data but also, recommends appropriate values for the missing ratings and overcome sparsity problem. The results of experiments are evaluated with three metrics: RMSE
¹
, NMAE
²
, and RE
³
. Results show that our approach leads to better prediction.