Radial Basis Function Network object
a=rbfnet(hyperParam)
Generates an rbfnet object with given hyperparameters. The used basis
functions are exp(-gamma*||x-z_i||) where gamma and z_i can be optimized
Hyperparameters (with defaults)
nr_of_centers=1 -- the number of centers to be used
init_with_kmeans=0 -- the centers are initialized with a kmeans
fixgamma=0 -- the variance is fixed. model parameter gamma
is used
maxiter=2000 -- number of maximal iterations
eps = 0 -- stopping criteria
Model
centers -- the centers used for basis functions
gamma -- estimated 1/2*variance^2 parameter
alpha -- final coefficients
Methods:
train, test
Example:
Estimate Sinc Function with Rbfnet and Bagged Rbfnet
t=[-5:0.29:5]';
ttest=[-5:0.06:5]';
y=sin(t)./t+1e-2*randn(length(t),1);
ytest=sin(ttest)./ttest+1e-1*randn(length(ttest),1);
d=data(t,y)
dtest=data(ttest,ytest)
rbn=rbfnet('nr_of_centers=3');
rbn.fixgamma=0; rbn.gamma=1e-3; rbn.eps=1e-5; rbn.init_with_kmeans =0;
rbn.maxiter=500; rbn.algorithm.use_signed_output=0;
a0=bagging(rbn,'bags=3');
a0.algorithm.use_signed_output=0;
[r,a]=train(group({rbn,a0}),d)
a1=a.child{1}; this was the rbf net
r=test(a1,dtest);
hold on;
plot(ttest,ytest,'.')
plot(ttest,r.X,'ro-');
loss(r,'quadratic_loss')
a2=a.child{2}; this was the bagged rbf net
r=test(a2,dtest);
plot(ttest,r.X,'b+-'); loss(r,'quadratic_loss')
legend({'true','Rbf','Bagged RBF'})
plot(a1.centers,a.centers*0,'rx')
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Reference : Neural Networks |