Research Of Sparse Subspace Clustering And Its Applications

With the rapid development of the Internet of Things technologies and the arrival of big data era,high-dimensional data are ubiquitous in the fields of image processing,pattern recognition,computer vision and machine learning,which poses a severe challenge to traditional clustering methods.Subspace clustering,as an important technology and method for dealing with high-dimensional data clustering problems,provides a way for the effective implementation of high-dimensional data clustering.In various subspace clus-tering methods,sparse representation based spectral-type clustering method has received extensive attention because of its superior clustering performance,easy processing and computational validity.It has become a research hotspot in subspace clustering,and been successfully applied to the problems of inlage representation,segmentation,motion seg-mentatiol and saliency detection.Aiming at some problems lying in the existing models,this thesis discusses and studies the improvement of sparsity,data error processing,effec-tive implementation of the algorithm,model extension and practical applications based on the framework of sparse representation with spectral method.The main contributions of this thesis are summarized as follows:1.The use of the l1 norm instead of the l0 one in sparse subspace clustering,can lead to a large deviation on large representation coefficients in some cases,which degrades clustering performance.To address the above problem,we propose a generalized non-convex approximation of the l0 norm and theoretically prove that it enables superiorly approximating the l0 norm than the l1 one.Moreover,the proposed generalized non-convex approximation incorporates commonly used approximations of the l0 norm into a unified structure,and simultaneously presents a large family of new ones.Inte-grating the proposed generalized non-convex approximation into subspace clustering,we propose a novel optimization formulation.Experimental results on synthetic data and real datasets indicate that the proposed generalized non-convex approximation helps to improve the clust ering performance.2.In practical applications,the clustering problems usually involve multiple variables and constraints,which easily cause over-complex algorithm analysis.To simplify algorit.hm analysis,we propose formulating different practical clustering problems in-volving multiple variables and constraints into a unified(0<p<1)minimization structure.In addition,a fast and effective iterative algorithm is developed for the proposed unified structure,with theoretically proved convergence.Experimental re-sults on synthetic data and real datasets further demonstrate the effectiveness of our method and model3.The discreteness of the l0 norm leads to the inability of general continuous optimiza-tion techniques for solving the l0 minimization problem,while employing the l1 norm instead of the l0 one can cause a looser relaxation in some cases.To address the problems,we propose a family of smooth approximation of the l0 norm,which can be applicable for the continuous optimization techniques,with better performance in approximating the l0 norm than the l1 one.Integrating the proposed smooth ap-proximation into subspace clustering,we propose a novel affine subspace clustering algorithm with improved clustering performance and robustness to noise.Moreover,a fast and effective iterative algorithm based on gradient descent and asymptotic pro-jection is proposed with the verified convergence.Extensive experiments on the real datasets demonstrate the effectiveness of the proposed method.4.Since the existing representation based spectral clustering methods usually cannot exclude the unimportant data points(In general,the unimportant data points refer to observations grossly corrupted by noise and extreme illumination conditions,or redundant samples)from participating in the representation of other data,this leads to a sub-optimal representation matrix and degrades the clustering performance.To overcome the above drawbacks,we propose a novel subspace clustering model which jointly minimizes the l1,2 and l2,1 norms.By imposing regularization on the representation matrix,the unimportant data points are excluded from participating in the linear representation of other data pointsj while enforcing the l2,1 regularization on the error matrix suppresses the impact of sample-specific corruptions(including outliers)lying in the data.This innovation leads to a superior representation matrix.By applying the spectral clustering method to the obtained representation matrix,we can obtain clustering assignments of data.The proposed algorithm is implemented using the Augmented Lagrange Multiplier(ALM)method.Its convergence is verified theoretically and experimentally.The merit of the proposed method is demonstrated in the process of handling two practical problems:motion segmentation and face clustering.