Research On Block Robust Tensor Principal Component Analysis Algorithm Based On Distance Measurement Learning

With the rapid development of information technology and the continuous improvement of computer computing capabilities,feature extraction for low-dimensional data of one-dimensional vectors and two-dimensional matrices can no longer adapt to the development of image processing,data analysis and dimensionality reduction.Scholars have extended these low-dimensional data feature extraction methods to high-dimensional tensor data and have been widely used in many fields such as face recognition,gait recognition,and hyperspectral images.On the other hand,in the process of image acquisition and image storage,affected by the image acquisition equipment,light intensity,sampling background,and image storage method,the samples will be contaminated to a certain extent.This requires the proposed algorithm to include noise data can reduce the influence of noise data on the entire sample data,that is,the algorithm has a certain robustness.In order to realize that the algorithm has a certain degree of robustness at the tensor level,this paper draws on the preprocessing method of block and conducts in-depth research on the robust tensor principal component analysis algorithm from the perspective of distance metric learning.The main research contents of this paper are as follows:(1)Multilinear PCA(MPCA)is not robust when solving the first k-order eigenvectors,and the robust tensor principal component analysis algorithm based on L₁norm(Robust tensor PCA with L₁-norm,TPCA-L₁-G)and non-greed(Robust tensor PCA with non-greedy L₁-norm,TPCA-L₁-NG)do not have the rotation invariance unique of F-norm.This paper selects F-norm as the distance metric learning method,and constructs the objective function from the perspective of the maximum projection distance.In view of the good performance of the block idea in principal component analysis,this paper first performs block operations on all data during preprocessing,and proposes a block robust tensor principal component analysis algorithm based on F-norm(Block Robust Tensor PCA with F-norm,Block TPCA-F).Experiments on GT and Aberdeen color face datasets show that Block TPCA-F can obtain more robust low-dimensional features than MPCA,TPCA-L₁-G and TPCA-L₁-NG.(2)The Block TPCA-F algorithm proposed in this paper only considers the maximum projection distance when constructing the objective function,and the maximum projection distance is not equal to the minimum reconstruction error.Therefore,from the perspective of the maximum projection distance and the minimum reconstruction error,this paper takes the ratio of reconstruction error and projection distance as the objective function,and proposes a block robust tensor principal component analysis algorithm(Block Robust Tensor PCA with proportion F-norm,Block TPCA-PF)based on proportion F-norm.It can be seen from the experimental results that Block TPCA-PF is more robust than Block TPCA-F and can extract more accurate low-dimensional features.(3)In this paper,Georgia Tech(GT)color face datasets and Aberdeen color face datasets are selected as experimental samples.In order to verify the robustness of the algorithm proposed in this paper,it is necessary to randomly select samples in the data set in advance and add a certain size of masking noise,and then conduct average reconstruction error experiment,image reconstruction experiment and classification rate experiment on the processed data set respectively.Considering the performance of the proposed Block TPCA-F and Block TPCA-PF algorithms in the experiment,the robustness of the proposed Block TPCA-F and Block TPCA-PF algorithms is further improved compared with the comparison algorithms.