performing a least squares with regularisation in matlab

25 次查看（过去 30 天）
cgo
cgo 2018-7-13
移动：Bruno Luong 2024-10-26，7:44
I have data sets X (2n by 8) and Y(2n by 1). I want to find the coefficients a so that Y = Xa. So we can perform a = X\Y (as a least squares minimisation).
I wanted to ask if it possible to proceed with a form of regularisation (L1 or something simple) from this?
Please help.
  1 个评论
SAKO
SAKO 2024-10-25，21:41
移动：Bruno Luong 2024-10-26，7:44
bonjours,je n'écris pas pour repondre a une question mais pour poser ma préoccupation.j'ai utiliser le package TOOL BOX de Per Christian Hansen pour faire une reconstruction de force.Avec la regularisation de Tikhonov pour le critère L_curve,le paramètre de regularisation qu'il me renvoi ne me permet pas de reconstruire ma force(ma courbe L_curve presente deux coins).Pouvez vous m'aider ?

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Diwakar
Diwakar 2018-7-13
My understanding of your problem is that you want to find the coefficient a. So in order to implement optimization you can implement average of sum of least squares as shown below.
Loss= ((Y-X*a)'*(Y-X*a))/(2*n);
The above shown function is a vectorized implementation of the squared error loss function. So this can be minimized in order to get the optimal value of a. If you want to fit a curve to this then any form of regularization should be fine.
Hope this helps
Cheers!
Bruno Luong
Bruno Luong 2020-9-23
编辑：Bruno Luong 2020-9-23
Simpless method:
n = size(X,2); % 8
lambda = 1e-6; % <= regularization parameter, 0 no regularization, larger value stronger regularized solution
a = [X; lambda*eye(n)] \ [Y; zeros(n,1)]

类别

在 Help Center 和 File Exchange 中查找有关 Mathematics and Optimization 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by