Research On The Application Of Matrix Completion In Recommendation Systems

Recent years,with the rapid development of the computer technology and Internet,the size of Internet users and content services is increasing by geometric orders of magnitude.The mass of information exceeds the range of personal acceptance,leading to the problem of information overload.Recommender system can mine effective information from massive data and save the time of users to search.It has become an effective method to solve the problem of information overload and has been applied in various fields.Matrix completion technology uses some known elements in matrix to recover other unknown elements,which can alleviate the problem of data sparsity in the recommendation system.This paper focuses on matrix completion and its application in the recommendation system as follows:(1)In the matrix completion model based on nuclear norm,the singular values of the matrix are treated equally and the approximation effect of nuclear norm to rank function is not good in practical application,which leads to low accuracy in the completion of the scoring matrix.To solve the above problems,we propose a matrix completion model based on weighted Schatten-p norm minimization.Firstly,Schatten-p norm was used as the surrogate of the rank function,leading to a low rank constraint.Then,the singular values are assigned different weights to approximate the original rank function better.Moreover,the proximal alternating linearized minimization is used to solve the non-convex minimization problem of matrix completion.At last,the experimental results on Movie Lens dataset show that the proposed model improves the accuracy of prediction and is superior to some typical and newly proposed model.(2)Aiming at the problem that the existing matrix completion model based on nuclear norm cannot exactly reflect the properties of the original matrix,a matrix completion model based on weighted truncated nuclear norm was proposed.First,different weights were assigned to the rows of the residual error matrix,and the rows with more observed entries were given smaller weights than others.Then,the truncated nuclear norm was used for achieving closer approximation of the rank function.Finally,the optimization problem was solved using the accelerated proximal gradient line search method(APGL).And we apply the proposed model to recommendation system rating prediction.The experiments of datasets show that the proposed method can achieve better prediction accuracy compared with some typical and newly proposed recommendation algorithms.