Probabilistic Matrix Tri-factorization And Its Applications

Matrix decomposition is a data analysis tool frequently used in computer vision,machine learning and data mining.In recent years,the probabilistic model of matrix decomposition has become the focus of attention.The existing probabilistic matrix decomposition usually decomposes the data matrix into the product of two low-rank matrices,which may limit the flexibility and practicability of the model.In this thesis,a robust model of probabilistic matrix tri-factorization and a bayesian probabilistic matrix tri-factorization model are established respectively.The main work of this thesis is as follows.Several classical probabilistic matrix factorization formulations and matrix tri-decomposition models are studied respectively.The probabilistic matrix factorizations mainly includes probabilistic matrix factorization,robust probabilistic matrix factorization,and bayesian probabilistic matrix factorization.The models and algorithms of these probabilistic matrix factorization and matrix tri-factorization are compared,and their advantages and disadvantages are described.Finally,the comparisons of these algorithms in image denoising and video background modeling are made.In order to enhance the flexibility and practicability of probabilistic matrix decomposition model,a robust probabilistic matrix tri-factorization model and a bayesian probabilistic matrix tri-factorization model are proposed in this thesis.The robust probabilistic matrix tri-factorization decomposes the matrix into the product of three matrices.Considering the robustness,an expectation maximization algorithm based on maximum a posteriori estimation is designed for solving the proposed model.In the experiments,robust probabilistic matrix tri-factorization is applied to imagedenoising and modeling of video background.The expermental results validate the feasibility and effectiveness of the proposed method.The tri-factorization of bayesian probabilistic matrix is also proposed and bayesian inference is used to infer model paramefers.Tri-factorization of bayesian probabilistic matrix is applied to image denoising and modeling of video background,the experimental results show that the model is feasible.