Research And Application Of A Fast Algorithm Based On Rotated L_2,1 Norm

Nuclear-norm minimization model and singular value thresholding algorithm are often used to extract and recover specific information from real-world data with high-dimensional and low-rank structures.However,the computational framework of these algorithms often depends on the weighted sub-gradient constructed by the exact singular value decomposition algorithm,which makes these algorithms easy to be limited in the actual calculation of processing large-scale data.To reduce computational cost,one way to improve the efficiency growth rate is to reduce the computational cost of solving the singular vector matrix precisely by using an effective dimensionality reduction matrix.However,how to select the appropriate dimension according to the data characteristics remains to be further studied.On this basis,the main work of this paper is as follows:This paper analyzes the spatial interpretation of the Left-rotated L_2,1norm and pro-poses a Left-rotated L_2,1norm minimization model to replace the nuclear norm model.The alternative model chooses a cheaper orthogonal algorithm to compute the subgradi-ent matrix.The LRN model is extended to matrix completion.To solve the LRN model,three methods are used to obtain the algorithms LRN-ADMM,LRN-APGL and LRN-ADMMAP.Besides,a comparison experiment is conducted with the nuclear norm model in the photo-graph.As the difficulty of image restoration increases,the LRN model has higher restora-tion quality,with lower computation time and cost.At the same time,the LRN model is applied to face recognition,and according to the constraints of the model,the algorithm LRN-R-ADMM and LRN-R-ADAMAP are solved by different methods.In the common face recognition database,the comparison experiment is carried out with the nuclear norm model algorithm.The experimental results show that the overall effect of the proposed algorithm is not much different or even slightly improved from that of the nuclear norm model algorithm,with reducing the computation time and cost.In the parameter experiment,the LRN algorithm has a more obvious effect of speeding up and improving efficiency,with stronger robustness to parameter changes.Considering that reducing the dimension of matrix singular value calculation can obtain a faster and more efficient decomposition algorithm,this paper proposes different rank pre-selection strategies for LRN models based on QR decomposition and Lanczos Process to better extract the appropriate subspace dimension and basis,and tests them in simulation data and image filling experiments.The experimental results show that the QR with Column Pivoting can better select the parameters of the matrix of different dimensions,rather than just rely on experience and attempt to select the calculated matrix.