A Study On Algorithms Of Matrix Recovery And Their Applications Based On The Truncated Norm

Matrix recovery has attracted great attention from many scholars in recent years,and a large number of algorithms and applications for low rank matrix recovery have emerged.In these algorithms,the nuclear norm is generally used to constrain the low rank part.However,due to the non-convexity and discontinuity of the rank function,which leads to the nuclear norm not being a well approximation to the rank function,so the application effect is often poor.Therefore,it is crucial to develop a robust and stable low rank matrix recovery algorithm.In view of the shortcomings of the existing matrix recovery algorithms,this thesis improves the corresponding algorithm and makes its algorithm model have better performance in application.It mainly studies salient object detection based on weighted Schatten p-norm and tree structured sparsity decomposition,algorithms and their applications for matrix recovery with truncated Schatten p-norm,and exclusivity regularized algorithm for multi-view low-rank sparse subspace clustering.The details are as follows.1.Salient object detection based on weighted Schatten p-norm and tree structured sparsity decomposition.For the problem of salient object detection,we propose a novel model based on weighted Schatten p-norm and tree structured sparsity decomposition.Firstly,we over-segment the image into patches to extract the image feature matrix.Secondly,the background priori of the image is extracted,and the image is divided into the image background and the salient object.Then,on the one hand,the weighted Schatten p-norm was used to constrain the background of the image.On the other hand,the salient object was constrained by tree structured sparsity norm and Laplacian regularization,to improve the accuracy of saliency detection.Finally,the model is solved by the alternating direction multiplier method.Extensive experimental results show that the proposed method has better detection performance comparing with four state-of-the-art detection methods on three different databases.2.Algorithms and their applications for matrix recovery with truncated Schatten p-norm.In order to improve the deficiencies caused by the nuclear norm-based algorithms,in the image restoration and background modeling problem,we propose a non-convex matrix completion model and a non-convex low-rank sparse decomposition model based on truncated Schatten p-norm.In solving the proposed models,firstly,the function expansion is used to transform the non-convex optimization model into a convex optimization model.Secondly,the two-step iterative algorithm based on the alternating direction multiplier method is used to solve the model.Then,through theoretical proof,the algorithm is convergent.Finally,the effectiveness and superiority of the algorithm based on truncated Schatten p-norm are illustrated by artificial data experiments and actual image experiments.3.Exclusivity regularized algorithm for multi-view low-rank sparse subspace clustering.For the multi-view subspace clustering problem,a large number of subspace clustering algorithms have been proposed to improve its clustering performance.However,the existing methods construct the affinity matrix and solve the multi-view subspace clustering problem by spectral clustering method on each view separately,and then select the best clustering result.This operation ignores the association between different views.In view of this,we propose a multi-view low-rank sparse subspace clustering method based on exclusive regularization.Firstly,the subspace representation coefficient matrix is subjected to low rank and sparse constraints.Secondly,the exclusive constraints of different coefficient matrix are used to learn an affinity matrix shared by all views.Then,the model is solved by the alternating direction multiplier method.Compared with state-of-the-art multi-view subspace clustering methods on several data sets,the proposed method achieves better clustering performance.