Research On Matrix Completion Based Recommend Algorithms

The recommendation system is an important research content of the fields of data mining.It can solve the problem of sudden decline in the effective utilization rate of information caused by information expansion,and has a wide range of applications for product recommendation.The recommendation system based on scoring matrix has defects such as data sparsity,uninterpretability,synonymousness and cold start.For the data sparse problem,the researchers use the low rank property to constrain the sparse matrix,and then find the solution of data matrix,and propose recommend algorithm based on matrix complementation technique.The thesis focuses on the problem of data sparsity and conducts research on the recommendation algorithm based on matrix completion.The follows are our main research work;1.Proposes a Mixed Linear Matrix Completion based Recommend Algorithm(MLMC-RA).The algorithm combines the characteristics of users and items and the relationship between themselves and the scoring matrix of users-items,constructs a recommendation model of mixed linear matrix completion,and theoretically analyzes the solution to the model,then gives proof of the global optimal solution to this algorithm.Simulation experiments and actual data experiments verify the effectiveness of the MLMC-RA algorithm.2.Proposes a Non-Linear Matrix Completion based Recommend Algorithm(NLMC-RA).The algorithm firstly uses the kernel principal component analysis method to extract some nonlinear features of the user-item scoring matrix,and fully exploits the high-order relationship between the user and other users,between the item and other items;The high-order relationship between users(items)is embedded in the MLMC-RA model to solve the matrix completion in the absence of auxiliary information,also could reduce the impact of shilling attack and guarantee the quality of recommendation.Experiments show the effectiveness of the algorithm.3.Proposes a Kernel Functional Matrix Completion based Recommend Algorithm(KFMC-RA).The algorithm aims to mine and utilize the implicit nonlinear relationship between users and objects.The kernel method is used to construct the recommendation model based on matrix completion,and solved in the corresponding inner product space.Furthermore,the model is optimized by the properties of Schatten p-norm,and the matrix is complemented and recommended accordingly.Experiments verify the effectiveness of the algorithm.