Research Of Matrix Decomposition Recommendation Algorithm Based On Trust Relationship

With the rapid development of Internet and e-commerce, information is in the state of overload. Compared to the traditional information retrieval search engines, personalized recommendation system provides another method to solve the problem of information overload. Through the analysis of the user's attribute information(gender, age, occupation, hobbies, etc.) and historical behavior information(user rating for the item, etc.), personalized recommendation system gets the interest preferences of users, and then initiatively recommends the related items and information to the users, in order to help the users to improve the quality and efficiency of finding information. Such as collaborative filtering recommendation, traditional recommendation algorithm is the most widely used and effective technique in the e-commerce website. Since it only takes into account the user-item rating, which is very sparse, the quality of the recommendation is not high. Meanwhile, the traditional recommendation algorithms exist the cold start problem, that is, the new user issues and the new item issues, as well as the anti-assault issues and the scalability issues. Thus, considering the fact that the users much prefer to choose or accept the goods or information recommended by the users' own friends, this thesis proposes two recommendation algorithms based on the users' trust relationship. Details as follows:Firstly, propose a recommendation algorithm based on the user trust relationship and probability matrix factorization(Trust-based Probability Matrix Factorization, TPMF).By decomposing the joint probability of the user trust relationship matrix and the user-item rating matrix, this algorithm gets the new user feature matrix, which satisfies the constraints of the user trust matrix and the user-item rating matrix simultaneously. After that, it makes inner product operation of the new user feature matrix and the item feature matrix, getting the missing values of rating and generating recommendation. Experimental results show that the proposed algorithm(TPMF) can alleviate the sparsity of user-item rating matrix to a certain extent, and improve the recommendation accuracy.Secondly, propose a recommendation algorithm based on the trust relationship and singular value decomposition(Trust-based Singular Value Decomposition++, TSVD++). Based on the singular value decomposition recommendation algorithm of user and item bias term simultaneously(Singular Value Decomposition++, SVD++), this algorithm integrates the user trust relationship, and then the model parameters are obtained by optimizing the target function. Next, the missing values of the user-item rating matrix are obtained through the user-item rating prediction formula, finally generating recommendation. The experimental results show that the proposed algorithm(TSVD++) can alleviate the sparsity of user-item rating to some degrees, and improve the recommendation accuracy.