Research On Collaborative Filtering Algorithm Based On Graph Construction And Matrix Factorization

With the development of information technology and the network, the data are growing day by day, and the speed of information dissemination is accelerated. It facilitates people's life, at the same time, brings the negative impact of information overload. How to extract information from the massive data in a timely manner has become the focus of attention. Recommendation system, as a kind of information filtering technology, can find the user's individual needs by digging the user's behavior, and deliver useful information in the information overload environment. It has become a hot spot of research.Recommendation algorithm is the core of the recommender system, in which collaborative filtering recommendation algorithm has attracted much attention from both academia and industry due to its high precision and expansibility. The recommendation problem based on rating data is one kind of important application problems. The researchers have done a deep research on the recommender algorithm and proposed effective collaborative filtering algorithms based on matrix factorization.In the collaborative filtering algorithm based on matrix factorization, to embed local similarity between users or items in the matrix factorization framework is an effective way to improve the performance of the recommendation algorithms. For this reason,researchers have studied a lot on how to embed the similarity between users or items in the framework of matrix factorization, but the research on the construction of matrix factorization and item similarity joint learning model is relatively few.Therefore,the thesis focuses on the recommendation of rating data, builds the collaborative filtering model by joint learning both local similarity and latent factor vectors. The main work is as follows:1. We propose a collaborative filtering algorithm based on matrix factorization with embedded items' similarity constraint (SI - GMF). The algorithm assumes that:(1) locally similar items have similar implicit semantic features; (2) the optimal solution of the item's similarity is within a certain neighborhood of the known item's similarity. Based on these assumptions, we construct the corresponding regularization items and embed them into the collaborative filtering algorithm model based on matrix factorization, and then obtain the effective similarities and implicit semantic feature vectors through joint learning. Experiments verify the effectiveness of the SI-GMF algorithm.2. We introduce a recommendation algorithm based on graph construction and matrix factorization (SO-GMF). The algorithm assumes that: (1) locally similar items have similar latent semantic features; (2) there is a certain degree of similarity between items and its neighbor items. According to these hypotheses, the SO-GMF algorithm describes the similarity degree of the items by the graph. The entropy constraint is used to overcome the degradation of the graph edge weight, and then the regularization term of the local preserving and entropy constraints are constructed and embedded into the matrix factorization model. SO-GMF algorithm learns the weight of graph and latent factor vector at the same time. The experimental results show that the SO - GMF algorithm improve the accuracy of recommendation.3. We present a recommendation algorithm (SO-SGMF) based on graph construction and L1 regular matrix factorization. Considering the sparsity of rating data, based on the assumptions of the SO-GMF algorithm, particularly, SO-SGMF assumes that the users' real rating obey the normal distribution, and the latent semantic factor matrix of the user and the item obey the Laplace distribution. Based on the above assumptions, we construct the regularization term of L1 term, local preserving and entropy constraints and embed them into the square error minimization function, and then obtain the weights of graph and latent semantic feature vectors effectively by joint learning. SO-SGMF algorithm can be adapted to the recommendation better in the situation of sparse rating data.