Zhang, "New results on Hermitian matrix rank-one decomposition," Math. Program. Ser. A, vol. 128, no. 1-2, pp. 253-283, Jun. 2011.W. Ai, Y. Huang, and S. Zhang, "New results on hermitian matrix rank- one decomposition," Mathematical Programming: Series A, vol. 128, pp. 253...
In this paper, we present several new rank-one decomposition theorems for Hermitian positive semidefinite matrices, which generalize our previous results in Huang and Zhang (Math Oper Res 32(3):758–768, 2007), Ai and Zhang (SIAM J Optim 19(4):1735–1756, 2009). The new matrix rank-one...
We introduce a rank-one and sparse matrix decomposition model for dynamic magnetic resonance imaging (MRI). Since $l_p$-norm $(0 < p < 1)$ is generally nonconvex, nonsmooth, non-Lipschitz, we propose reweighted $l_1$-norm to surrogate $l_p$-norm. Based on this, we put forward a...
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of applications in model and system identification, and is ...
However, many existing algorithms are not scalable to large-scale problems, as they involve computing singular value decomposition. In this paper, we present an efficient and scalable algorithm for matrix completion. The key idea is to extend the well-known orthogonal matching pursuit from the ...
1) rank one decomposition 秩1分解 1. By using therank one decompositionmethod and Kronecker multiplication method the proof of r(A * B)≤r(A)r(B) is presented. 讨论了矩阵Hadamard乘积的一些性质,分别用秩1分解法和Kronecker乘积法给出了r(A*B)≤r(A)r(B)的证明。
Cucuringu. Uniqueness of low-rank matrix completion by rigidity theory. SIAM Journal on Matrix Analysis and Applications, 31(4):1621–1641, 2010. Article MathSciNet Google Scholar G. Tang and P. Shah. Guaranteed tensor decomposition: A moment approach. In Proceedings of The 32nd International...
1. A linear iterative method for projective reconstruction based on rank 1 matrix containing the images of all points in all views,which can deal with all the images in a unified manner,is presented in the paper. 提出了一种能够将所有图像平等看待基于秩1的射影重建方法,该方法并不是直接求解射...
rankuses a method based on the singular value decomposition, or SVD. The SVD algorithm is more time consuming than some alternatives, but it is also the most reliable. The rank of a matrixAis computed as the number of singular values that are larger than a tolerance. By default, the toler...
(higher-ordertensor),一般提到的张量都是特指高阶张量目录1稀疏张量的分解 1.1Tucker分解(具体可以参考https://zhuanlan.zhihu.com/p/24798389...参数 3相关论文TensorDecompositionsandApplicationsTensorDecomposition for Signal Processingand 笔记:Tensor RPCA: Exact recovery of corrupted low-rank tensors via conve...