Visual Information Analysis Based On Sparse Representation And Manifold Learning

Most of the external information obtained comes from the visual function.How to make the computer with excellent performance having the visual function like people and be able to analyze the information obtained by the visual function is the aim of computer vision.Image classification is a major research topic in the field of computer vision.It's widely used in face recognition,image compression,weapon system,intelligent traffic,unmanned driving,etc.Image classification is a typical high-dimensional data supervised learning problem.Extracting effective information to represent images is an important prerequisite and key to image classification.Sparse representation and manifold learning are effective means for feature extraction of high-dimensional data.In this dissertation,the sparse representation based on high-dimensional data and the feature extraction method of manifold learning are discussed,and the task of image classification is achieved by constructing a linear classifier.The classical method of sparse representation of high-dimensional data is realized by establishing the optimization problem of 0-norm of feature matrix.But the optimization problem of 0-norm is NP-hard problem,it's usually to obtain the optimal convex hull of0-norm-1-norm to realize sparse feature extraction of high-dimensional data.However,the optimization objective function of 1-norm optimization problem is a piecewise differentiable function,which can only obtain numerical solution,which makes sparse representation coefficients can't represent or reconstruct test samples well.Although the 2 norm is the optimal global differentiable extension of the 1 norm,the sparse representation method based on the 2 norm can only constrain that each sparse representation coefficient is very small,but can not guarantee that the sparse representation coefficient corresponding to the training sample which is different from the test sample is small,and the sparse representation coefficient corresponding to the training sample which is similar to the test sample is larger.Aiming at this problem,a sparse representation method based on weighted 2-norm is proposed in the third chapter,but the sparse representation method based on weighted 2-norm can only deal with one test sample at a time,so a sparse representation method based on sample heterogeneity is proposed to deal with multiple test samples.After mathematical deduction,the analytical solutions of two improved methods are obtained,and the efficiency of the two improved methods is verified by experiments.Because of the sparse representation method based on the sample dissimilarity proposed above only considers keeping sparse of sparse representation coefficients and constrained optimization objective function is the problem of global differentiability.It didn't consider the similar test sample should've the similar coefficients of sparse representation and similar training samples should've similar reconstruction effects on the same type of test samples,which makes the sparse representation coefficients of similar test data are quite different,the similar training samples have different reconstruction effects on the same kind of test samples.To settle it,in chapter 4,a sparse representation method based on Laplacian Eigenmaps is proposed.By mathematical deduction,this dissertation gets the iteration formula of sparse representation method based on Laplacian Eigenmaps,and proves the convergence of the iterative formula.The effectiveness of the sparse representation method based on Laplacian Eigenmaps is verified by experiments.