Research Of Recommend Algorithm Based On Approximate Matrix Decomposition

With the rapid development of social and science technology, information on the Internet is explosive growing. People nowadays have involved in massive amounts of data, leading to the searching of information difficult. When exposed to massive products with amounts of descriptions, users are amused to choose what they are interesting in. To solve this situation, recommend the commodity to user may function in the process of surfing the Internet. Thus, the recommend algorithm appear to recommend products users may interesting,The algorithm putted forward in this paper is a algorithm that recommend products based on the approximating matrix factorization. The algorithm is proposed in two process, the first is the preprocessing of data based on fuzzy clustering and the second is the recommendation based on the approximating matrix decomposition algorithm. In the first step, this paper studies the properties of entropy and further we propose an algorithm that partition nodes into different clusters. This paper puts forward a new definition of membership function as well as an authority scores based on PageRank. Combining all those algorithm, we propose the fuzzy cluster algorithm to partition the data into k clusters and reduce the size of data. In the second step of recommend, we deal with the clusters attained in the first step.. At first, we change the definition of problems in the Relaxation principle. Thus, the problem of matrix factorization is a problem of semi-definite programming. Deal with the solution of the semi-definite programming, we apply Cholesky principle to decompose the matrix to get what we need. In the solving of the recommend problem, we apply the Lagrange method to solve the problem.This paper study the core technology of recommend problem, that is, the relationship analysis between user and products. To solve the problem, we study the recommend problem from the perspective of mathematics. We propose an effective recommend algorithm to recommend relative products to users. The experiment results show that the algorithm we proposed solve the recommend problem effectively.