The Sparse Coding Model And Its Application

Because high-dimensional data often belongs to several low dimensional subspaces,highdimensional data can be linearly represented by a few atoms.Sparse coding is an efficient representation of high-dimensional data,the purpose is to use a linear combination of a small number of atoms to approximate the input data,and requires atoms with data adaptability,which is atoms can characterize some essential features of the data.Because of its advantages of high efficiency for high-dimensional data representation,sparse coding has been widely used in image processing,speech signal separation,pattern recognition and so on.Over the development of sparse coding,the classic sparse coding model mainly considers coding sparsity constraints which can reflect the inherent low-dimensional features of the data,and some other works consider other properties of sparse coding,such as sparse structure,packet sparse and so on.In addition to the sparsity,this paper mainly considers how to use the linear correlation or similarity between data to guide the sparse coding,the purpose is to hope that the sparse coding can reflect these features of the data.This paper establishes a reasonable mathematical model and an efficient numerical algorithm for this problem,and make theoretical analysis and numerical experiments on the model and algorithm.On this basis,this paper discusses the application of models and algorithms in high-dimensional data clustering.The high-dimensional data clustering divides the data according to the subspace in which the data resides to reveal the low-dimensional subspace structure of the high-dimensional data.The main work of this paper includes: First,a new sparse coding model called Weight Local Sparse Coding is proposed by using the linear correlation or similarity between data to guide sparse coding.The representation coefficient matrix of this model has a good structure conducive to clustering,which is a better way to solve the subspace clustering problem.Under the theoretical support,a large number of experiments and evaluation indicators show that the proposed model have achieved a good clustering results in international standard image clustering dataset.Second,a new unified optimization model called Structured Sparse Low Rank Subspace Clustering is proposed,by defining a new subspace structured low rank regularity and incorporating it into the Structured Sparse Subspace Clustering model.The new model uses the estimated cluster membership of the samples and the affinity of the samples to guide each other,so that the affinity possesses both discrimination and coherence and the cluster membership has coherence property,which is advantageous to segment data from different subspaces into different clusters while group data from the same subspace into the same cluster.The clustering experiments were carried out on international standard image clustering dataset,and the performance of the model was analyzed by the evaluation index.The results show that the proposed model outperforms the state-of-the-art two-stage methods and the SSSC method.Good model of sparse coding is not only the basis of effective clustering,but also the assurance of further research application.