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dc.contributor.authorYuan, Ganzhao
dc.contributor.authorZheng, Wei-Shi
dc.contributor.authorShen, Li
dc.contributor.authorGhanem, Bernard
dc.date.accessioned2019-04-28T13:15:22Z
dc.date.available2019-04-28T13:15:22Z
dc.date.issued2018-06-07
dc.identifier.urihttp://hdl.handle.net/10754/632539
dc.description.abstractComposite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized optimization as special cases. This paper proposes and analyzes a new Generalized Matrix Splitting Algorithm (GMSA) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Our algorithm is derived from a novel triangle operator mapping, which can be computed exactly using a new generalized Gaussian elimination procedure. We establish the global convergence, convergence rate, and iteration complexity of GMSA for convex problems. In addition, we also discuss several important extensions of GMSA. Finally, we validate the performance of our proposed method on three particular applications: nonnegative matrix factorization, $\ell_0$ norm regularized sparse coding, and $\ell_1$ norm regularized Dantzig selector problem. Extensive experiments show that our method achieves state-of-the-art performance in term of both efficiency and efficacy.
dc.description.abstractComposite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized optimization as special cases. This paper proposes and analyzes a new Generalized Matrix Splitting Algorithm (GMSA) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Our algorithm is derived from a novel triangle operator mapping, which can be computed exactly using a new generalized Gaussian elimination procedure. We establish the global convergence, convergence rate, and iteration complexity of GMSA for convex problems. In addition, we also discuss several important extensions of GMSA. Finally, we validate the performance of our proposed method on three particular applications: nonnegative matrix factorization, $\ell_0$ norm regularized sparse coding, and $\ell_1$ norm regularized Dantzig selector problem. Extensive experiments show that our method achieves state-of-the-art performance in term of both efficiency and efficacy.
dc.description.abstractComposite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized optimization as special cases. This paper proposes and analyzes a new Generalized Matrix Splitting Algorithm (GMSA) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method and the Successive Over-Relaxation method for solving linear systems in the literature. Our algorithm is derived from a novel triangle operator mapping, which can be computed exactly using a new generalized Gaussian elimination procedure. We establish the global convergence, convergence rate, and iteration complexity of GMSA for convex problems. In addition, we also discuss several important extensions of GMSA. Finally, we validate the performance of our proposed method on three particular applications: nonnegative matrix factorization, $\ell_0$ norm regularized sparse coding, and $\ell_1$ norm regularized Dantzig selector problem. Extensive experiments show that our method achieves state-of-the-art performance in term of both efficiency and efficacy.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1806.03165v1
dc.relation.urlhttp://arxiv.org/pdf/1806.03165v1
dc.rightsArchived with thanks to arXiv
dc.titleA Generalized Matrix Splitting Algorithm
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.eprint.versionPre-print
dc.contributor.institutionKey Laboratory of Machine Intelligence and Advanced Computing, \nMinistry of Education, Beijing 221143, China.
dc.contributor.institutionSchool of Data and Computer Science, Sun Yat-sen University (SYSU), Guangzhou, Guangdong 510275, China
dc.contributor.institutionTencent AI Lab, Shenzhen, China.
dc.identifier.arxivid1806.03165
kaust.personGhanem, Bernard
dc.versionv1
refterms.dateFOA2019-04-28T14:03:58Z


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