Collaborative Filtering Based on Orthogonal Non-negative Matrix Factorization

Abstract

In order to study the application of orthogonal nonnegative matrix factorization (ONMF) in collaborative filtering, so as to improve the recommendation accuracy of collaborative filtering, firstly, the theoretical knowledge of the existing matrix factorization model was analyzed and discussed, and then linearization correction was added to the matrix factorization model. Secondly, orthogonal constraints were added to the traditional weighted non-negative matrix factorization model (WNMF) to make the algorithm decompose the original data into non-negative matrices. Finally, the NMF collaborative filtering algorithm based on unit factorization and graph regularization correction (RTGNMF) was proposed. Three models, RTGNMF, positive ONMF and WNMF, were compared in NMAE/RMSE on real simulated data sets. The results show that once Tikhonov is used to correct the parameters in NMF model in single graph, the RMSE value will continue to decline based on the parameter adjustment of D1 dataset. RTGNMF, ONMF and WNMF all change the recommendation performance of high-dimensional data to a certain extent. ONMF has higher recommendation accuracy than WNMF. The robustness and adaptability of RTGNMF, ONMF and WNMF decrease in turn. RTGNMF and ONME make up for the shortcomings of current collaborative filtering algorithms to a great extent, and have obvious advantages over traditional algorithms. Adding linear correction in the iteration process of matrix factorization can converge and oscillate progressively, and adding orthogonalization constraint can significantly improve the redundancy of data and effectively improve the recommendation accuracy of collaborative filtering.