How to implement the Gaussian radial basis function in MATLAB ?

8 vues (au cours des 30 derniers jours)
charu shree
charu shree le 20 Mar 2023
Modifié(e) : Torsten le 21 Mar 2023
Hello all, I am dealing with the following optimization problem
where is a column vector of dimension , is also a column vector of dimension , is matrix of dimension , is row vector of and is the Gaussian radial basis function, where is the variance.
My query is how to code this Gaussian radial basis function (RBF) ?
Any help in this regard will be highly appreciated.

Réponse acceptée

Torsten
Torsten le 21 Mar 2023
Modifié(e) : Torsten le 21 Mar 2023
Before you start the optimization, check whether K in your case is positive-definite.
Lt = 10;
p = rand(Lt,4);
sigma = 1.0;
for l = 1:Lt
for j = 1:Lt
K(l,j) = exp((norm(p(l,:)-p(j,:)))^2/(2*sigma^2));
end
end
K
K = 10×10
1.0000 1.0558 1.2332 1.1752 1.1144 1.7121 1.4345 1.4970 1.3174 1.4356 1.0558 1.0000 1.1059 1.1852 1.0453 1.4602 1.3978 1.2603 1.1884 1.3441 1.2332 1.1059 1.0000 1.4993 1.1769 1.7198 1.2359 1.2245 1.2960 1.8679 1.1752 1.1852 1.4993 1.0000 1.3279 1.1864 1.5427 1.3336 1.2247 1.0896 1.1144 1.0453 1.1769 1.3279 1.0000 1.6242 1.4504 1.5273 1.1608 1.4210 1.7121 1.4602 1.7198 1.1864 1.6242 1.0000 1.7290 1.2760 1.2118 1.1176 1.4345 1.3978 1.2359 1.5427 1.4504 1.7290 1.0000 1.5769 1.2315 1.9993 1.4970 1.2603 1.2245 1.3336 1.5273 1.2760 1.5769 1.0000 1.4254 1.5342 1.3174 1.1884 1.2960 1.2247 1.1608 1.2118 1.2315 1.4254 1.0000 1.2412 1.4356 1.3441 1.8679 1.0896 1.4210 1.1176 1.9993 1.5342 1.2412 1.0000
eig(K)
ans = 10×1
-1.7051 -0.8915 -0.6203 -0.3001 0.0081 0.0171 0.0346 0.0637 0.1039 13.2897
  6 commentaires
charu shree
charu shree le 21 Mar 2023
Ok....Thank you sir...
Torsten
Torsten le 21 Mar 2023
Modifié(e) : Torsten le 21 Mar 2023
Thank you for the correction.
Is it somehow obvious that the matrix will be positive-definite ?

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Plus de réponses (1)

Matt J
Matt J le 21 Mar 2023
Modifié(e) : Matt J le 21 Mar 2023
If you have the Statistics Toolbox, you can avoid a loop by using pdist2
Lt = 10;
p = rand(Lt,4);
sigma = 1.0;
K=exp(-pdist2(p,p).^2 / 2/sigma^2);

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