Probabilistic Tensor Decomposition And Its Applications

With the rapid development of information technology,the scale of data has expanded rapidly,resulting in a more complex high-dimensional data structure.In the process of data acquisition,some elements are commonly missing or contaminated by noise.Low-rank tensor recovery completes missing elements and discovers low-rank components based on the approximate low-rank structure of data.It has become a hot spot in the field of computer vision,data mining,machine learning and so on.The rank minimization framework is usually employed to solve low-rank tensor recovery problems.This framework has a high computational complexity and can not provide the probability distributions of the low-rank and noise components.To overcome the aforementioned shortcomings,this thesis proposes a Bayesian probabilistic tensor CP decomposition model with Laplace noise.The main contents of this thesis are as follows.Tensor CP and Tucker decompositions are two classical decomposition paradigms,and the corresponding probabilistic tensor decomposition models are investigated.Tensor CP decomposition includes: Bayesian tensor CP decomposition,Bayesian tensor CP decomposition,Beta binomial tensor CP decomposition,MCMC Bayesian tensor decomposition,multiplicative gamma process tensor decomposition and multiviews tensor decomposition.Tensor Tucker decomposition is composed of exponential family tensor decomposition and infinite Tucker tensor decomposition.These probabilistic tensor decomposition models are compared,and their advantagesand disadvantages are pointed out.To enhance the robustness of the probabilistic model of tensor decompositions,the Laplace noise is taken consideration into a Bayesian tensor CP decomposition model.Firstly,the data tensor is decomposed into the sum of a low-rank component and a noise term,and the noise is assumed to be Laplacian.Then a Bayesian tensor CP decomposition model is established.Next the variational Bayesian method is proposed to infer the model parameters.Subsequently,the lower bound of the evidence L(q)and the prediction model are deduced respectively.Finally,experiments are carried out on artificial datasets and natural image datasets.The experimental results show that the proposed method has better recovery performance.