Research On Algorithm Of Graph Regularized Nonnegative Robust Tensor Ring Decomposition And Application In Feature Extraction

With the progress of social science,more and more large-scale and high-dimensional data are produced in our daily life.These data tend to be physically significant and non-negative,which we call non-negative tensor data.There are a lot of valuable non-negative information in non-negative tensor data,as a result,feature extraction of non-negative tensor data is a necessary means to analyze and mine potential information.In the field of feature extraction,non-negative tensor decomposition is an effective method for feature extraction.It can directly characterize tensor data,therefore,it is widely used by researchers.However,it is difficult for the classical non-negative tensor decomposition algorithm to learn the manifold structure information in the high-dimensional tensor data,so that the extracted features cannot keep the manifold structure information of the data,which affects the performance of feature extraction.In addition,in the real world,data pollution by noise is also a common phenomenon,noise will seriously affect the discrimination of traditional non-negative tensor decomposition algorithm extraction features.Therefore,how to effectively deal with polluted non-negative tensor data and learn manifold structure information in high-dimensional tensor data is a thorny problem.Based on the Nonnegative Tensor Ring Decomposition(NTR),we propose a graph regularized nonnegative robust tensor ring decomposition.NTR decomposition algorithm can preserve the structure of non-negative tensor data to a certain extent and avoid"dimensional disaster"to a large extent.However,NTR decomposition algorithm cannot learn manifold structure information in high-dimensional tensor data.Considering that preserving data manifold structure can enhance the discrimination of extracted features,this thesis combines manifold learning technology and NTR decomposition algorithm,which can keep the manifold structure information of extracted features and improve the feature extraction performance of the whole algorithm model.Considering that real data is susceptible to noise pollution,we use_2,1 norm to fit the model,and then establish a robust joint optimization function.This thesis uses multiplier updating method,and the algorithm is called the graph constrained non-negative robust tensor ring decomposition algorithm,which is called L2,1-GNTR decomposition algorithm.Experiments show that L2,1-GNTR algorithm can well extract low-dimensional features from high-dimensional data,and has strong robustness,good convergence and parameter insensitivity in polluted data sets,and has strong practicability.Although L2,1-GNTR algorithm can well extract low-dimensional features of high-dimensional data,its constructed neighbor graph still requires artificial selection of hyperparameters,and sometimes it cannot accurately learn manifold structure information in high-dimensional tensor data,which limits the performance and practicability of the algorithm to a certain extent.In order to solve this problem,this thesis uses the concept of multi-graph decomposition to replace the single graph constraint and establishes the objective function.In this method,the linear combination of multiple graphs is used to construct the regularizer,and the weight of each graph can be determined adaptively without introducing additional parameters,for better explore the manifold structure information of data.Based on the multiplier updating method,the objective function is optimized in this thesis,and the algorithm is called multi-graph based robust non-negative tensor ring decomposition algorithm,called L2,1-MGNTR decomposition algorithm.Experiments show that L2,1-MGNTR algorithm is superior to L2,1-GNTR algorithm in both effectiveness and robustness of feature extraction.The graph constrained non-negative robust tensor ring decomposition algorithm proposed in this thesis can effectively extract features from non-negative tensor data with noise pollution,which provides a solution to the difficulty of feature extraction from non-negative tensor data with noise pollution and has strong practical significance.