Under the background of the rapid development of Internet technology, although the implementation of cloud computing, in large part, can provide data and information sharing platform,the explosive growth of data is still a large problem. In the era of big data,information overload problems still baffle the academic circles. The ability of recommender systems to generate connections between users and items makes them an important tools for alleviating information load. How to analyze and forecast in data mining is the core of large data processing. This paper devotes to the study of prediction of the collaborative filtering recommendation algorithm. With high prediction accuracy, good scalability, the integration graph model, manifold learning model, matrix factorization,especially nonnegative-matrix factorization model has been widely employed to solve the problems such as dimension reduction, computer vision and pattern recognition.Combining single-element-based method with graph and manifold approaches broadens the areas of other problems who expect to touch the effectiveness of other kind of constraints of manifolds and graph regularization.In the second chapter, after reading an in-depth exploration and study in the existing theory of matrix factorization, we added the linearization correction to matrix factorization in the basic model. It can be seen from a large number of existing documents, adding a linear correction to matrix factorization can overcome oscillations that occur during gradual convergence of the iteration and improve prediction accuracy in collaborative filtering recommendation coupled with the orthogonal correction and normalized to some extent avoid data redundancy. As it can be seen from the experimental results, integrating matrix factorization and orthogonal linear correction can achieve high prediction accuracy than m traditional collaborative filtering algorithm benchmark.At the conclusion of the first chapter, we find that BOMF do not take user and item features information into account which is of great importance and these implicit information in collaborative filtering recommendation algorithm can be improve the recommendation accuracy to a large extent. Taking into account the non-negative characteristic of most of the data, we summarize the existing data characteristics using the framework based on non-negative matrix factorization. In algorithm design, we integrate the single-element-based learning, Tikhonov correction, graph similarity correction to collaborative filtering. Based on single-element-based, graph non-negative matrix regularization, we proposed RTGNMF, is to make full use of the model-based collaborative filtering and memory-based collaborative filtering advantages. In addition, a single-element-based learning strategies can effectively evade the frequent manipulations,which lack of practicability.The research of Graph-based algorithm is far more than enough in CF problems, let alone the manifold structure analysis of data in the field of collaborative filtering algorithm. In the field of computer vision, graph regularization can be a good learning strategy, which can better inherent nonlinear structure information data. The manifold model has a good overall closed loop optimal solution compared with graph-based NMF. With the consideration, in the third chapter, we focus our NMF-based graphical models on the manifold regularization. However, different from the current NMF in solving the problems in computer vision, we also adopt single-element-based strategy to RGMMF because of the extreme sparsity of target rating-matrix. The idea is also to evade the frequent manipulation and lack of practicability. |