K-sparse Coding Based On Lp-box ADMM

With the high-speed development of modern information technology,people can be very convenient to obtain all kinds of information and data through a variety of sensing equipment and computer network.Data is exploding,it affects every aspect of human society deeply.How to analysis the valuable information from the massive amount of data is a very important subject.It also can work well in the Internet,sales,security,transportation,medical,and many other areas.Dealing with large-scale high imension data effectively needs to be solved urgently.Sparse coding can decrease the difficulty of storage through the study of the sparse representation of information and has the research value and potential huge application value in dealing with high-dimensional large data.As a cross sparse coding involves in neurobiology,psychology and computer science,and many other research fields.The deepening research of sparse coding theory suggests that the theory has the advantages of large storage which is widely used in signal and image processing,pattern recognition and other fields in the practical application,and theory can promote the further development of artificial intelligence.This article proposes a ksparse coding(k-SC)method to obtain the coding with specific k-sparsity,that is to say,select k simples with the smallest reconstruction error from the data set of the dictionary adaptively.It uses lp-box ADMM to deal with the problem of integer sparse optimization which is usually NP-hard.First,we transform the original integer sparse coding problem into 0-1 integer programming problem.Then the 0-1 integer constraint conditions is replaced with the equivalent two consecutive constraint conditions,and the new optimization problem is solved by the alternating Direction method of Multipliers(ADMM)algorithm.This article proves that ADMM based on lp-box is effective in the k-sparse coding problem by the convergence and accuracy of the algorithm experiments on different datasets.