Research On Low Dimensional Representation Algorithm Of Robust Tensor Based On Distance Measurement Learning

With the rapid development of science and technology,low dimensional representation of tensor data features is broadly applied to image processing,data dimension reduction and other fields,the traditional low dimensional representation methods based on vector and matrix data have been unable to meet the current demand.In the process of high-dimensional data acquisition and transmission,the data sample often contains polluted noise due to the influence of equipment accuracy,environmental illumination and data storage mode.Therefore,it requires the algorithm to reduce the sensitivity to noise structure in the process of data processing,that is,the algorithms have robustness.In order to improve the robustness of tensor algorithm,this paper studies the robust tensor principal component analysis algorithm based on low dimensional representation from the perspective of distance measurement and optimization objective of the algorithm’s objective function.The main contents of this paper are as follows:(1)By studying the geometric projection principle of tensors,this paper builds a triangular projection model of tensors with F norm,which satisfies the "Pythagorean Theorem".Furthermore,four objective function(sine,cosine,tangent and area)are proposed.The objective function also considers the biobjective optimization task of maximum projection distance and minimum reconstruction error.Compared with the existing robust tensor principal component analysis algorithm,the proposed algorithm has better robustness in the low dimensional representation of tensor features.According to the four objective functions of the triangular tensor projection model,this paper applies the block recombination technique to the tensor data in the preprocessing stage,including robust Block Tensor PC A with F norm projection sine algorithm(sinBTPCA-F),cosine algorithm(cos-BTPCA-F),tangent algorithm(tan-BTPCA-F)and area algorithm(area-BTPCA-F)have been proposed.At the same time,the detailed solving algorithm and steps of the objective function are given,and the convergence and rotation invariance of the algorithm are proved by taking the tangent algorithm as an example.Finally,according to the noise conditions of experiment and the block parameters of algorithm,different parameter experiments are designed,including the noise parameter experiment,block parameter and reconstruction error experiment,block parameter and classification rate experiment.The optimal block parameters under different experimental conditions are discussed,so as to create conditions for the subsequent comparison experiment.(2)In this paper,the application conditions of F norm and Nuclear norm are further discussed,and the different effects of nonlinear factors such as the difference of environmental background information between samples on Nuclear norm and F norm are proved theoretically,and the experimental verification is carried out.Therefore,this paper proposes robust Tensor PCA with Nuclear Norm(TPCA-Nuclear).For the problem that the Nuclear norm is difficult to solve,this paper converts the Nuclear norm measurement in the objective function into F norm,and gives two solving methods,the iterative method and the direct method.In order to ensure the fairness of the experiment with the comparison algorithm,this paper chooses the iterative method to conduct the subsequent comparison experiment.(3)Seven international standard color data sets were selected as experimental samples and artificial noise blocks of different proportions were randomly added to them.The average reconstruction error,image reconstruction and classification rate experiments were carried out on the processed datasets respectively.The experimental results show that the proposed robust BTPCA with F norm projection(sine,cosine,tangent,area)and the robust TPCA with Nuclear norm have significantly improved robustness compared with the existing algorithm.