Study On Sparse Graph Subspace Learning Algorithms

Manifold learning and sparse representation are important research topics in computer vision,pattern recognition and image processing,which have been attracted many attentions by researchers in recent decades.The basic assumption of manifold learning is that the feature representation of image in high dimensional space often contains lower dimensional manifold structure.As one of the classical methods of subspace learning,graph learning can reveal the manifold structure in high-dimensional data space by describing the relations between each pair of samples,which has become a vivid topic in recent years.Sparse representation is actually a kind of decomposition of the original signal process;the decomposition process uses a prior complete dictionary to present the input signal as a linear approximation of the prior complete dictionary.Inspired by these two methods,this paper will focus on the use of sparse representation of the sample and the construction of sparse graph for describing datasets,combined with theories of subspace learning,non-negative matrix decomposition,discriminant analysis,and regression technique.It is of great theoretical and practical significance to study the method of graph construction based on sparse representation and its application in image classification.The contributions of this thesis are as follows:1)We proposed Sparse Graph regularized Nonnegative Matrix Factorization(SGNMF)to overcome the shortcomings of nonnegative matrix factorization in the application of pattern recognition and data mining,which did not consider the intrinsic geometric structure of the data.SGNMF algorithm firstly constructs a sparse graph to describe the relationship between each pair of samples by sparse representation,and uses this graph to replace the graph in GNMF algorithm which is constructed by nearest neighbor.It uses Laplacian feature map to deduce the Laplacian moment of sparse graph L.Finally,combined with the manifold learning method,if the point and are near in the original space,then the corresponding coordinate and in the new base must be close,to define a regularization term adds to the nonnegative matrix factorization as a regularization term.Due to the merits of the sparse representation,the algorithm is better able to describe the relationship between samples.2)We proposed Sparse Graph Linear Discriminant Analysis(SGLDA)learning algorithm to solve the problem of the image feature extraction in subspace,which combines with sparse representation and traditional Linear Discriminant Analysis algorithm.Linear Discriminant Analysis(LDA)algorithm lacks information to handle the small size samples.As a semi-supervised method,the SGLDA algorithm affords a complete geometry description by adding a regularization term which consists of all data,provides a pre reference for the selection of projection subspace,so that the SGLDA can solve the problem of small sample size well.At the same time,the SGLDA algorithm uses sparse representation to construct the data structure relations among samples,which increases the robustness of resisting noise,and makes it able to deal with the feature extraction taskes.3)We introduce a constraint of the relationship between each pairs of classes to propose a Category Guided Sparsity Preserving Projection(CGSPP)to overcome the shortages of Sparse Preserving Projection(SPP)algorithm and Locality Preserving Projection(LPP)algorithm only preserving the relationship of samples and ignoring the relationship of classes.CGSPP algorithm explores the relationship between the categories,keeps more origin data features to cast latent subspace structure,enhance the robustness and discrimination ability of the extracted features.At the same time,the affinity matrix is based on sparse representation,which has stronger robustness to noise.4)We propose a Collaborative Sparse Preserving Projection(CSPP)algorithm combining sparse representation and collaborative graph embedding model.In CSPP,sparse representation algorithm is used to construct a sparse graph with a higher robustness to represent the relation between samples,and the-norm constraint is added to enhance the discrimination ability and robustness of data.The CSPP algorithm combines the advantages of sparse representation and collaborative representation to enhance the robustness of sparse graph regularization algorithm,at the same time the learned regression coefficients are more smoothly,and improves the computational efficiency of the model in applications.Compared with other subspace learning algorithms in several famous databases,the results of the experiment show our algorithms are more superior.