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Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations [PDF]
IEEE Transactions on Neural Networks and Learning Systems, 2018 A lot of works have shown that frobenius-norm based representation (FNR) is competitive to sparse representation and nuclear-norm based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism.
Xi Peng, Zhang Yi, Canyi Lu
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On a Conjecture Concerning the Frobenius Norm of Matrices
Linear and Multilinear Algebra, 2012The purpose of this article is to discuss the conjecture on the Frobenius norm of matrices. The conjecture on the Frobenius norm of matrices proposed by Sloane and Harwit is proved for a class of special matrices.
Limin Zou
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Perturbation Bounds of Core Inverse Under the Frobenius Norm
Bulletin of the Malaysian Mathematical Sciences Society, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuefeng Gao
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2020 IEEE 4th Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), 2020
PCA is a classical feature extraction method. But PCA usually loses the structure information of the image. As the tensor version of PCA, 2DPCA could save the structure information and could be fast calculated. However, both PCA and 2DPCA utilize the square of Frobenius norm to describe the total scatter, which enlarges the influence of the outliers ...
Wei Wang, Wencong Ruan, Qiang Wang
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PCA is a classical feature extraction method. But PCA usually loses the structure information of the image. As the tensor version of PCA, 2DPCA could save the structure information and could be fast calculated. However, both PCA and 2DPCA utilize the square of Frobenius norm to describe the total scatter, which enlarges the influence of the outliers ...
Wei Wang, Wencong Ruan, Qiang Wang
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The Extremum of the Frobenius Norm of Matrix
2011 Fourth International Joint Conference on Computational Sciences and Optimization, 2011For two given matrices A and B, the extremum of the Frobenius norm of matrix B-XA is established when X is running all over the unitary matrices. By using the technique of singular value decomposition, the extremum of the Frobenius norm matrix is studied. The result shows that the matrix B-XA has extremum when X is running all over the unitary matrices
Kai-Fan Yang
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Is the Frobenius matrix norm induced?
IEEE Transactions on Automatic Control, 1995Remind that the Frobenius norm of the matrix \(A\) with the items \(A_{\mu\nu}\) is \((\sum_\mu \sum_nu|A_{\mu\nu}|^2)^{1/2}\). From the authors' abstract: ``using the notion of dual norms we show that, up to a scalar multiple, the maximum singular value is the only unitarily invariant induced norm. As a special case of this result, it follows that the
VijaySekhar Chellaboina +1 more
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Probabilistic Analysis of an Estimator for the Frobenius Norm of a Matrix Product
JSIAM Letters, 2017 Summary: Estimating the Frobenius norm of a matrix product \(C=XY\) without computing \(C\) explicitly is required in applications such as the one-sided block Jacobi method. In this paper, we analyze \textit{M. Bečka} et al.'s [Parallel Comput. 28, No.
Yusaku Yamamoto
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Frobenius norm minimization and probing for preconditioning
International Journal of Computer Mathematics, 2007In this paper we introduce a new method for defining preconditioners for the iterative solution of a system of linear equations. By generalizing the class of modified preconditioners (e.g. MILU), the interface probing, and the class of preconditioners related to the Frobenius norm minimization (e.g.
T. Huckle, A. Kallischko
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Joint Frobenius norm and reweighted nuclear norm minimization for interference alignment
2013 IEEE International Conference on Communications (ICC), 2013This paper considers a K-user multiple-input multiple-output (MIMO) interference channel in which uncoordinated interference appears. Due to the uncoordinated interference, perfect interference alignment (IA) may be not attained, which indicates the interference subspaces can not be completely aligned.
Huiqin Du +3 more
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Some Natures on Matrix Frobenius Norm
2010 Third International Conference on Information and Computing, 2010In this paper, some natures of Frobenius norm are obtained by using majorization, which can be used in numerical mathematics and matrix perturbation analysis.
Zhiying Ding
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