Research On Collaborative Filtering Recommendation Algorithm Based On Schatten-p Norm

With rapid development of Internet and mobile technology,it has provided people with mass of data and information.How people pick and choose whatever information they're interested in has become the main problem which recommender system tries to solve.Collaborative filtering technology is currently one of recommendation algorithms applied widely.Among them,the matrix factorization algorithm has especially received worldwide attention of scholars.Matrix factorization algorithm utilises low rank approximation of sparse rating matrix to estimate unrated data.In order to solve overfitting problem because of sparsity,the regularization term is a common method.This paper focuses on matrix factorization model based on Schatten-p norm regularization term,and introduces it to collaborative filtering recommendation algorithm.Data sparse,cold start problems are the main challenge recommendation system has fased.Transfer learning is a effective method to solve these problems.Transfer learning utilize auxiliary information to help the learning tasks in the target field.In recommendation system,users(items)are not completely consistent in both auxiliary domain and target domain so that the users(items)features may not be completely consistent.Therefore,many feature transfer methods cannot directly be applied to recommendation system.In view of this situation,this paper will study transfer learning model with the aid of Schatten-p norm to help predict rates within target domain.In this paper,the main research includes the following two aspects:(1)A matrix factorization model based on Schatten-p norm regularization term is put forward to solve the rating prediction problem.In real applications,the sparsity of different rating matriies is different.In addition,some baleful evaluation or shilling attack also can reduce the reliability of the ratings matrix.As a result,a single matrix factorization model is difficult to generalize in several different data sets.So,this paper constructs loss function of the q-th power in the training set and use the Schatten-p norm constructs regularization term.Further,we provide iterative algorithm about q=1,q=2 and q=3,and the algorithm was derived theoretically and validated.Since each iteration only with "sparse + low rank" of the structure of the matrix singular value calculation,the algorithm also has a good applicability for large-scale data.Through multiple actual data set,we verify the validity of the algorithm in this paper.(2)This paper proposes an transfer learning model based on Schatten-p norm,used to predict ratings data within target domain.First,we use previous algorithm extract users' or items' features of auxiliary rating matrix.Next,an novel transfer learning model is proposed by using user/item characteristic structure based on Schatten-p norm,connecting with the loss function on the target training data.The model makes the user/item in target domain and auxiliary a certain similarity so that it can transfer the features of auxiliary field to the target domain.Further,this paper puts forward to the effective algorithm to solve the transfer model.This algorithm has several obvious advantages: 1)without requiring the dimension of auxiliary domain and target domain,reduced the demand for data sets;2)make full use of the advantages of Schatten p norm,each iteration only with "sparse + low rank" of the structure of the matrix singular value calculation,suitable for large-scale matrix;3)algorithm parameters less.Compared with several non-transfer and tansfer collaborative filtering algorithm in different experiment,we verify the effectiveness of the transfer learning algorithm proposed in this paper.