Research On Latent Sparse And Low-rank Representation And Its Applications

In dealing with complex high-dimensional data,subspace representation algorithms can restore the real subspace structure of data,and play an important role in image clustering,image classification,image segmentation,dynamic segmentation and image compression.Sparse subspace representation is used to extract local characteristics of data by imposing sparse constraints on coefficient matrices,and low-rank subspace representation is used to obtain global characteristics of data by imposing low-rank constraints on coefficient matrices.These two algorithms are typical algorithms in data subspace representation.However,sparse or low-rank representation algorithm only uses column space information of data,ignores the importance of row space information,and is not effective in dealing with data with insufficient samples or polluted by noise.In this paper,sparse representation and low-rank representation are studied in depth.On the basis of inheriting the advantages of sparse and low-rank representation,two new algorithms are proposed for hyperspectral image classification,face clustering,classification and multi-modal image fusion.1)In this paper,a latent low-rank graph discrimination analysis(LatLGDA)is proposed by considering both row and column space information in data.The row and column representation coefficient matrices in data subspace are constrained by low-rank to obtain the optimal representation coefficient matrices.Then the projection matrix is solved by the graph embedding model,and the high-dimensional data is mapped to the low-dimensional space to realize the feature extraction of hyperspectral data.Finally,the data classification results are obtained by using support vector machine.Compared with sparse and low-rank representation algorithms,LatLGDA algorithm can extract more abundant data features by combining row and column space information with graph embedding model,which is helpful to improve subspace representation ability and data classification.2)A latent sparse joint low-rank representation(LSLRR)is proposed,in which sparse constraints and low-rank constraints are applied simultaneously to the column representation coefficient matrix in data subspace representation.On the basis of inheriting the advantages of sparse and low-rank representation,sparse and low-rank are effectively combined to preserve both local and global characteristics of data while restoring the real subspace structure of data.Clustering and classification experiments on face data sets and image fusion experiments on multi-modal image data sets verify the validity of LSLRR.