The Research On Nonlinear Signal Classification Problem Based On Sparse Representation Theory

In recent years,sparse representation theory has achieved good application effects in many fields,and it is an effective signal processing method.However,at present,most of the research is still focused on the linear cases.There are a lot of nonlinear cases in the practical application,although it is very difficult to analyze and process the nonlinear signals both conceptually and computationally.In order to promote the research on such problems,this paper will take nonlinear signals as the research object and propose algorithms with good performance in sparse coding and dictionary learning.The two main research works of this paper are as follows:1)Research on nonlinear sparse coding algorithm based on Lasso.Inspired by the independent interpretable Lasso method(IILasso),the third chapter puts forward the following two algorithms:(?)Combining IILasso with kernel function,propose the kernel independent interpretable Lasso algorithm(KIILasso);(?)On the basis of(?),the lp norm(0<p<1)is introduced into the regularization part of the algorithm,and the kernel independent interpreatable weighted Lasso algorithm(KIIWLasso)is proposed to improve the sparsity and precision of the sparse vector.The proposed algorithms are applied to synthetic data,gene expression data and handwritten digital datasets,and their advantages are verified.Among them,KIILasso performs best on handwritten digital datasets,while KIIWLasso performs best on synthetic data and gene expression data.2)Research on nonlinear dictionary learning algorithm based on analysis sparse model.Analysis sparse model can minimize the dependence on each atom and thus stabilize the recovery process.At present,there are still very few discussions on nonlinear dictionary learning methods based on this model.Therefore,in the fourth chapter,we combine the kernel method with the analysis sparse model and propose two effective nonlinear dictionary learning methods based on the kernel technique.The first method firstly converts the nonlinear problem into a linear form based on the kernel transformation method,which still retains the nonlinear information of the original problem,and then solves the dictionary based on the linear dictionary learning algorithm.In the second method,a nonlinear dictionary learning algorithm is proposed based on the KSVD-like framework.The algorithm takes advantage of the sparsity of the high-dimensional data to obtain the analysis dictionary from the dataset effectively,and applies the proposed method to solve the nonlinear classification problem.The benchmark experiments on USPS,MNIST and E-YaleB datasets show that the second algorithm outperforms some related linear and nonlinear dictionary learning algorithms.The accuracy of the first algorithm is slightly lower than that of the second one,but it is still superior to other related algorithms.Moreover,the second algorithm is also effective when the data is interfered by noise or some pixels are missing,which proves that it has good robustness.