Tensor Completion Model Via Nonconvex Tensor Ring Rank Minimization

With the rapid development of computer networks and artificial intelligence,the amount of data is increasing exponentially.The data in various fields presents the characteristics of high-order,such as image restoration,social network and so on.We can gain more valuable information by analyzing the complex structural characteristics and the physical meaning of these data.However,data can be lost during the process of collection or transmission.So recovering high-order missing data has become one of the research topics in the field of infor-mation technology.As a typical representative of high-order data processing,tensor decom-position has unique natural advantages.Many models based on low-rank tensor representation have been proposed and widely used in artificial intelligence,pattern recognition and image classification.In recent years,there has been a lot of research and discussion about tensor ring decom-position.Because it can excavate the low-rank representation of tensors,retain the spatial structure information and effectively avoid the dimensional disaster.Aming at the problem of high-order data missing,this thesis research nonconvex optimization low-rank tensor ring completion model based on tensor ring decomposition.In this paper,two kinds of rank min-imization models of tensor rings based onL_Pnorm constraint are proposed,and two corre-sponding efficient optimization algorithms are designed respectively.They are applied to the completion task of tensor data,which compared with other tensor completion algorithms to verify the efficiency of the proposed method.The model of tensor ring kernel norm has some errors in approximating TR rank.This method treats every singular value equally and ignores its physical meaning,which often leads to suboptimality of solutions in practical applications.To solve this defect,we chooseL_Pnorm for rank minimization,which is closer than the kernel norm.We proper a nonconvex tensor ring model(L_P)based onL_Pnorm.In particular,this method imposesL_Pnorm constraint on TR expansion matrix,which makes the model approximate TR rank more accurately.The weighted singular value threshold algorithm is applied to improve the low rank of the model solution.In order to effectively solve the proposed non-convex model,the alternate direction multiplier method(ADMM)is used to update and optimize the model.Experimental results on both color image and video data demonstrate the effectiveness of theL_Pmethod,compared with other tensor completion algorithms.This method has enough generality which can be extended to other tensor factorizations to develop more efficient and robust algorithms.In order to solve the problem of high computational loss in large-scale tensor completion,this thesis propose a tensor ring completion model(L_P)based on the potential TR factor.The rank minimization problem of a tensor ring is translated to a potential TR core of much smaller scale,which massively reduces the computational loss of tensor ring rank minimiza-tion.In particular,by the operation of tensor ring decomposition,the low-rank constraint ofL_Pnorm is applied to the matrix of each tensor TR factor expansion.We establish the efficient tensor ring rank minimization model and solve the problem of manually selecting the rank of a tensor ring effectively.This thesis uses alternating direction multiplier method to update and optimize the model.Finally,the experimental results on different types of data demonstrate the superiority of theL_Pmethod over other tensor completion methods.