Based On Graph Regularization Low Rank Matrix Algorithm And Its Applications

In the current information explosion,the acquisition and processing of information is particularly important.How to deal with the large or repetitive image data is the current research hotspot.The low rank matrix algorithm is a kind of excellent algorithm in this field.The traditional low rank matrix algorithm takes the whole structure information of the input matrix into account,but ignores the internal structure information of the input matrix,so the graph regularization is introduced.The graph regularization is to compute the minimum trace of the matrix,which is the product matrix of the input matrix and its graph Laplacian matrix.The research content of this paper is to introduce graph regularization on the basis of low rank matrix algorithm to enhance the low rank of the recovery matrix.The specific work is as follows:First,the Matrix Completion(MC)algorithm mainly uses the known information in the matrix to fill the unknown information.In this paper,the based on graph regularization matrix completion algorithm(GMC)is studied.Experimental data shows that the proposed algorithm has significantly improved image restoration effect compared with traditional matrix filling algorithm and block matrix filling algorithm.Secondly,the Robust Principal Component Analysis(RPCA)algorithm makes up for the regret that the PCA can not solve the non-Gaussian noise problem,but its recovery effect still needs to be improved.In this paper,the graph regularization is introduced into the RPCA algorithm,and the image blocking strategy is used to further improve the recovery effect.The experimental data show that the Based on Graph Regularization Robust Principal Component Analysis(GRPCA)has advantages over the RPCA in image denoising and video background separation experiments.Finally,the Low-Rank Representation(LRR)algorithm is the idea of introducing a dictionary representation in a sparse representation on a RPCA algorithm.The algorithm hopes that the coefficient matrix of the restored dictionary is a low-rank matrix.In this paper,by introducing the graph regularization to increase the low rank property of the matrix.In order to make the nuclear norm better close to the real rank of the matrix,a weighted matrix is introduced to a Based on Graph Regularization Weighted Low-Rank Representation(GWLRR)algorithm.Experimental data shows that the proposed algorithm outperforms other algorithms in image clustering.