Abstract: Missing value estimation of sparse matrix is a necessary basic research,which is also particularly important and significant in some practical applications,such as the recommendation system.There are many methods to solve this problem,one of the most effective method to tackle this issue is Matrix Factorization (MF).However,the traditional MF algorithm has some limitations,which can only directly simulate the elements of the sparse matrix by using regression method.But it did not take into account the sample itself,which has different difficulty in regression and should be treated respectively.According to this limitation,this paper proposed a matrix factorization recommendation algorithm based on adaptive weighted samples (AWS-MF).Based on the traditional MF algorithm,the proposed method exploits the differences among the training samples and treats each sample in a bias weights.In order to improve the performance and robustness of our model,the intermediate results are combined together in the final process to obtain the objective predictions.To verify the superiority of the proposed method,the comprehensive experiments were conducted on the real-world data sets.The experiment results demonstrate that the proposed AWS-MF algorithm is able to adaptively re-weight samples according to the differences among them.Moreover,treating the samples respectively can lead to a promising performance in the real-world applications compared to the baseline methods.

Key words: Bias, Matrix Factorization(MF), Missing value estimation, Recommendation system, Sample differences