Nonnegative Tensor Decomposition Methods For Transition Matrix Modeling In Collaborative Filtering

With the large-scale popularization of the mobile Internet,increasing information and ever-changing business models put people in a dilemma of information overload.As a tool to help users filter out more effective information,the recommendation system has been accelerated development in academia and industry.In order to analyze user behavior preference data more accurately,collaborative filtering has become an important technical tool,and model-based collaborative filtering has been the focus of research in recent years.Among them,the matrix-based decomposition model and the tensor-based decomposition model can learn from sparse large-scale data well,and the variants of these models consider more detailed user preference characteristics.However,we found through literature research that there is no work to explore the connection between the tensor factorization model and the matrix factorization model.The conventional Frobenius norm constraint cannot fully describe the dynamic changes of user preferences over time.The latent vectors obtained by tensor decomposition has been lack of explanation.Therefore,this paper starts from the basic properties of nonnegative tensor decomposition,reveals the mathematical connection between the tensor decomposition model and the sequential matrix decomposition model,and gives a reasonable explanation to the latent vector.Based on these findings,we propose two new nonnegative decomposition models to deal with the time-aware collaborative filtering problem.The specific work is as follows:First of all,based on the nature of CP decomposition,this article mathematically derives the relationship between the sequential matrix decomposition model and the tensor decomposition model,and connects the user preference transition matrix and the time latent vector.Thus,preliminary work has been done for the interpretability of time latent vectors.Secondly,after a new understanding of time latent vector,we propose a temporal similarity based nonnegative tensor decomposition model.This new model can take into account more details of user preferences changing with time.We also developed an efficient algorithm for the new model.Next,we discuss the relationship between CP decomposition and Tucker decomposition in modeling transition matrix,and propose a core sparse nonnegative tensor decomposition model.Tucker decomposition is used to enrich the interaction between hidden vectors,and the sparse constraint is added to the core tensor of Tucker decomposition,which together ensure that the new model can automatically determine the interaction strength between hidden vectors through the optimization algorithm.It is a data-driven method and reduces the intervention of artificial prior knowledge.Finally,this paper verifies the effectiveness and advantages of the models and algorithms proposed in this paper on multiple public data sets,and opens the source code for our algorithms.