net = rbftrain(net, options, x, t) uses a
two stage training
algorithm to set the weights in the RBF model structure net.
Each row of x corresponds to one
input vector and each row of t contains the corresponding target vector.
The centres are determined by fitting a Gaussian mixture model
with circular covariances using the EM algorithm through a call to
rbfsetbf. (The mixture model is
initialised using a small number of iterations of the K-means algorithm.)
If the activation functions are Gaussians, then the basis function widths
are then set to the maximum inter-centre squared distance.
For linear outputs, the hidden to output weights that give rise to the least squares solution can then be determined using the pseudo-inverse. For neuroscale outputs, the hidden to output weights are determined using the iterative shadow targets algorithm. Although this two stage procedure may not give solutions with as low an error as using general purpose non-linear optimisers, it is much faster.
The options vector may have two rows: if this is the case, then the second row
is passed to rbfsetbf, which allows the user to specify a different
number iterations for RBF and GMM training.
The optional parameters to rbftrain have the following interpretations.
options(1) is set to 1 to display error values during EM training.
options(2) is a measure of the precision required for the value
of the weights w at the solution.
options(3) is a measure of the precision required of the objective
function at the solution. Both this and the previous condition must be
satisfied for termination.
options(5) is set to 1 if the basis functions parameters should remain
unchanged; default 0.
options(6) is set to 1 if the output layer weights should be should
set using PCA. This is only relevant for Neuroscale outputs; default 0.
options(14) is the maximum number of iterations for the shadow
targets algorithm;
default 100.
net = rbf(1, 4, 1, 'gaussian'); options(1, :) = foptions; options(2, :) = foptions; options(2, 14) = 10; % 10 iterations of EM options(2, 5) = 1; % Check for covariance collapse in EM net = rbftrain(net, options, x, t);
rbf, rbferr, rbffwd, rbfgrad, rbfpak, rbfunpak, rbfsetbfCopyright (c) Ian T Nabney (1996-9)