Low-Rank Representation (LRR) has been a popular tool for identifying data generated from a union of subspaces. It is also known that LRR is computationally challenging. As the size of the nuclear norm regularized matrix of LRR is propor... S Jie,L Ping,H Xu - 《Statistics》 被引量: ...
MATRIX decompositionFor a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP d...
The matrix with r1 as both its first and second row has a determinant of 0, so you can get rid of it. Eventually you'll get to matrices with determinant 0 or matrices consisting of some permutation of r1, r2, and r3, whose determinant will be either +det(A) or -det(A). When yo...
The problem of computing a real matrix perturbation having a minimum norm which causes a general complex matrix to drop rank is examined. Given the state model describing a linear time-invariant system, the norm of this matrix perturbation helps to determine the robustness of several system propert...
r is the rank of A. Best k-rank approxmation We minimize ||A - D_k||_F among all matrix D_k with rank \leq k. The best approxmation is D_k = \sum_{t=1}^k A v^{(t)} v^{(t)^T} = \sum_{t=1}^k \sigma_t u^{(t)} v^{(t)^T} \\ This means the subspace...
However, to find the inverse of the matrix, the matrix must be a square matrix with the same number of rows and columns. There are two main methods to find the inverse of the matrix: Method 1: Using elementary row operations Recalled the 3 types of rows operation used to solve linear ...
We consider the linear Hankel matrix H(x) = H0... D Henrion,S Naldi,SED Mohab - ACM 被引量: 10发表: 2015年 Real root finding for low rank linear matrices The problem of finding low rank m 脳 m matrices in a real affine subspace of dimension n has many applications in information...
(or just naive method). another method that relies on finding a null vector of a matrix is described in [ 41 ], whose matrix elements are defined via the divided differences. analyzing stability for this method appears to be complicated and is an open problem. 2.2 chebfun’s ratinterp ...
Mulmuley, K.: A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Comb. 7(1), 101–104 (1987). https://doi.org/10.1007/BF02579205 24. Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4), 541–580 (1989) 25...
We assume that each data point can be expressed as a linear combination of the representatives and formulate the problem of finding the representatives as a sparse multiple measurement vector problem. In our formulation, both the dictionary and the measurements are given by the data matrix, and ...