问题: 求∂‖A∘(Y−W⊤X)‖F2∂W和∂‖A∘(Y−W⊤X)‖F2∂X,其中,∘表示Hadamard product,各变量均为矩阵形式。 求解: 为方便起见,定义Z=A∘(Y−W⊤X),同时,将F-norm重写为Frobenius product(详见备注)的形式,则有: ∂‖A∘(Y−W⊤X)‖F2=∂Z:Z=2Z:dZ=2Z:d...
∂f(x)∂xxT=xxT∘Y∂f(x)∂xxT=xxT∘Y but I do not know how to actually compute this w.r.t.xx. I am pretty inexperienced with this kind of thing, so any input would be really helpful. Thank you! matrices derivatives ...
3.2. Frobenius Norm. Let f : R q×p →R be defined as f(B) = ||B|| 2 F . f(B +∆) = B +∆, B +∆ = B, B +2 B, ∆ + ∆, ∆ = f(B) +2 B, ∆ +||∆|| 2 F Thus, we see that derivative of f at B is a function ∆ →2 B, ∆...
Numerical results show the advantages of our model on the test set considered, and the derivative-free algorithms based on our least $H^{2}$ norm updating quadratic model functions can solve test problems with fewer function evaluations than the algorithm based on the least Frobenius norm ...
We address bilevel programming problems when the derivatives of both the upper- and the lower-level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is sm...
Summary: A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of ... A Ziehe,M.K.A.W.A.M. Abe,S. Harmeilng - 《Journal of Machine Learning Research》 被引量: 399发表: 2004年 Low Complexity Damped...
Using the two classical choices of the Barzilai-Borwein parameters, two positive parameters were derived by minimizing the distance between the relative matrix corresponding to the propose search direction and the scaled memory-less Broyden–Fletcher–Goldfarb-Shanno (BFGS) matrix in the Frobenius norm....
minimum Frobenius norm since β = 2 x,x m(x) F . While other “minimal norm” quadratics could be found, we are drawn to those with Hessians of minimal norm because the resulting solution procedure will have a natural tie-in to fully linear models. The KKT conditions for (3.3) can...
of the sample set, the dimensions of the problem and polynomial space, and the number of sample points. We consider linear and quadratic determined models and underdetermined quadratic models, particularly Minimum Frobenius Norm models. We extend some classical results by considering a relaxed ...
Recently, a derivative-free optimization algorithm was proposed that utilizes a minimum Frobenius norm (MFN) Hessian update for estimating the second deriv... R Brmen,T Tuma,J Olenek 被引量: 0发表: 2021年 Computer system and process for explaining behavior of a model that maps input data ...