A new Approach for Building Recommender System Using Non-Negative Matrix Factorization Method

Nonnegative Matrix Factorization is a new approach to reduce data dimensions. In this method, by applying the nonnegativity of the matrix data, the matrix is ​​decomposed into components that are more interrelated and divide the data into sections where the data in these sections have a specific relationship. In this paper, we use the nonnegative matrix factorization to decompose the user ratings matrix in recommender systems. The user ratings matrix is factorized in a way that the users with similar interests can be identified.
In this paper, we used a regularization method to minimize the difference between the main matrix and the factorized components. To this end we insert the coefficients which are defined as the norm of the decomposition factors in the factorization equation. The coefficients control the entries of the decomposition factors in a multiplication update process. Our numerical results on the MovieLens data set represent the greater accuracy of our proposed method in predicting user ratings for items.