Research On Low-rank Completion Models Based Tensor

Data representation is preparatory work for data processing.Matrix and vector are the commonly used representation methods.With the development of the information age,the data present multidimensional trend.Traditional matrix-based data analysis is twodimensional,which limits the utilization of information from a multi-dimensional perspective.On the other hand,tensor-based models can take advantage of the multi-linear structure of data.Therefore,tensor is the main topic in this thesis.The data often appears missed and lost in the processing of data collecting,collating and storing,resulting from equipment precision,human operation,weather environment and time.Tensor completion is to predict missing elements based on properties of observed data.Obviously,completion becomes infeasible without relationship between missing and observed.Fortunately,symmetry,continuity and repeatability often exit between the data.At present,models and theories for tensor completion are focused on how to define the rank of tensor.For low-rank matrix completion,the classical methods are based on the convex relaxation of matrix rank by the nuclear norm.However,global information of observed data can be used and local characteristics be neglected,if the tensor nuclear norm directly used as the measurement of low-rank.Furthermore,solving the tensor optimization problems often deviates the original problem solution.Meanwhile,it is not appropriate to treat different singular values equally.Based on the exiting modes and theories,this thesis proposes a novel low-rank tensor completion model called low-rank tensor completion model based on weighted schatten-p norm and orthogonal dictionary learning.Firstly,different weights are assigned according to the importance of different singular values.Then,the weighted tensor schatten-p norm is used to describe the global structure of the data.Regarding discovery of the local patterns of data,an orthogonal dictionary learning process is incorporated into spare coding.Finally,the experiment results demonstrate the effectiveness of proposed model on the public database with Augmented Lagrange Method.