矩阵的2-范数(2-norm of a matrix) 向量u∈Rnu∈Rn 的2范数,即其欧式空间长度为: ∥u∥2=uTu.‖u‖2=uTu. 矩阵H∈Rm×nH∈Rm×n 的2-范数相应为: ∥H∥2=max∥u∥2=1∥Hu∥2.‖H‖2=max‖u‖2=1‖Hu‖2. 这个东西可以被证明是矩阵 HTHHTH 的最大特征值的平方根,即 HH 的最大奇异值...
2-norm 的求导 引用:normed spaces - Derivative of norm 2 - Mathematics Stack Exchange 有两种方法,链式法则+常规的从对每个向量求导出发: 方法1 方法2
metric space- a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc. ...
Random MatrixL{sub}2 NormThis work furnished a sharper bound of exponential form for the L{sub}2 norm of an arbitrary shaped random matrix. Based on the newly elaborated bound, a non-uniform sampling method was developed to succinctly approximate a matrix with a sparse binar...
The induced matrix 2-norm in ?3.Intuition might suggest that the euclidean vector norm should induce theFrobenius matrix norm (5.2.1), but something surprising happens instead.Matrix 2-Norm•The matrix norm induced by the euclidean vector norm is?A?2= max?x?2=1?Ax?2=?λmax,(5.2.7)...
NORM_LARGEST_SUM = 1 : the largest column sum of matrix or the 1-norm NORM_LARGEST_SINGULAR = 2 : the largest SVD of matrix NORM_INFINITY = 3 : the largest row sum of matrix NORM_FROBEBINUS = 4 : the Frobenius-norm of matrix, sqrt(sum(diag(pData'*pData)))Return...
4) matrix 2-Norms 矩阵2-范数 1. A theorem on matrix 2-Norms is proved in this short note,which could be used to mathematically analyze some kind of algorithms in image processing in the future. 证明了矩阵2-范数的一个定理。5) 2-norm deviation 2-范数偏差...
Synchronization in time-varying networks: A matrix measure approach Synchronization in complex networks has attracted lots of interest in various fields. We consider synchronization in time-varying networks, in which the we... Chen,Maoyin - 《Physical Review E Statistical Nonlinear & Soft Matter Phys...
Experiments on benchmark face datasets demonstrate the effectiveness of our presented method in comparison to the state-of-the-art methods. 展开 关键词: Nonnegative matrix factorization Local constraint Clustering DOI: 10.1007/s11042-017-4970-9 ...
Here, the bounds of a matrix norm of a rectangular matrix are given. This matrix norm is wider than the p-matrix norm (1≤p≤+∞). We have ?? In addition, the necessary and sufficient eonditions for ‖A‖_p‖A~(-1)‖_p=1(1≤p≤+∞) are obtained, and the necessary and suff...