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06 Nov 2002 (Updated )

Pattern analysis toolbox.

rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)
function net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)
%RBF	Creates an RBF network with specified architecture
%
%	Description
%	NET = RBF(NIN, NHIDDEN, NOUT, RBFUNC) constructs and initialises a
%	radial basis function network returning a data structure NET. The
%	weights are all initialised with a zero mean, unit variance normal
%	distribution, with the exception of the variances, which are set to
%	one. This makes use of the Matlab function RANDN and so the seed for
%	the random weight initialization can be  set using RANDN('STATE', S)
%	where S is the seed value. The activation functions are defined in
%	terms of the distance between the data point and the corresponding
%	centre.  Note that the functions are computed to a convenient
%	constant multiple: for example, the Gaussian is not normalised.
%	(Normalisation is not needed as the function outputs are linearly
%	combined in the next layer.)
%
%	The fields in NET are
%	  type = 'rbf'
%	  nin = number of inputs
%	  nhidden = number of hidden units
%	  nout = number of outputs
%	  nwts = total number of weights and biases
%	  actfn = string defining hidden unit activation function:
%	    'gaussian' for a radially symmetric Gaussian function.
%	    'tps' for r^2 log r, the thin plate spline function.
%	    'r4logr' for r^4 log r.
%	  outfn = string defining output error function:
%	    'linear' for linear outputs (default) and SoS error.
%	    'neuroscale' for Sammon stress measure.
%	  c = centres
%	  wi = squared widths (null for rlogr and tps)
%	  w2 = second layer weight matrix
%	  b2 = second layer bias vector
%
%	NET = RBF(NIN, NHIDDEN, NOUT, RBFUND, OUTFUNC) allows the user to
%	specify the type of error function to be used.  The field OUTFN is
%	set to the value of this string.  Linear outputs (for regression
%	problems) and Neuroscale outputs (for topographic mappings) are
%	supported.
%
%	NET = RBF(NIN, NHIDDEN, NOUT, RBFUNC, OUTFUNC, PRIOR, BETA), in which
%	PRIOR is a scalar, allows the field NET.ALPHA in the data structure
%	NET to be set, corresponding to a zero-mean isotropic Gaussian prior
%	with inverse variance with value PRIOR. Alternatively, PRIOR can
%	consist of a data structure with fields ALPHA and INDEX, allowing
%	individual Gaussian priors to be set over groups of weights in the
%	network. Here ALPHA is a column vector in which each element
%	corresponds to a separate group of weights, which need not be
%	mutually exclusive.  The membership of the groups is defined by the
%	matrix INDX in which the columns correspond to the elements of ALPHA.
%	Each column has one element for each weight in the matrix, in the
%	order defined by the function RBFPAK, and each element is 1 or 0
%	according to whether the weight is a member of the corresponding
%	group or not. A utility function RBFPRIOR is provided to help in
%	setting up the PRIOR data structure.
%
%	NET = RBF(NIN, NHIDDEN, NOUT, FUNC, PRIOR, BETA) also sets the
%	additional field NET.BETA in the data structure NET, where beta
%	corresponds to the inverse noise variance.
%
%	See also
%	RBFERR, RBFFWD, RBFGRAD, RBFPAK, RBFTRAIN, RBFUNPAK
%

%	Copyright (c) Ian T Nabney (1996-2001)

net.type = 'rbf';
net.nin = nin;
net.nhidden = nhidden;
net.nout = nout;

% Check that function is an allowed type
actfns = {'gaussian', 'tps', 'r4logr'};
outfns = {'linear', 'neuroscale'};
if (strcmp(rbfunc, actfns)) == 0
  error('Undefined activation function.')
else
  net.actfn = rbfunc;
end
if nargin <= 4
   net.outfn = outfns{1};
elseif (strcmp(outfunc, outfns) == 0)
   error('Undefined output function.')
else
   net.outfn = outfunc;
 end

% Assume each function has a centre and a single width parameter, and that
% hidden layer to output weights include a bias.  Only the Gaussian function
% requires a width
net.nwts = nin*nhidden + (nhidden + 1)*nout;
if strcmp(rbfunc, 'gaussian')
  % Extra weights for width parameters
  net.nwts = net.nwts + nhidden;
end

if nargin > 5
  if isstruct(prior)
    net.alpha = prior.alpha;
    net.index = prior.index;
  elseif size(prior) == [1 1]
    net.alpha = prior;
  else
    error('prior must be a scalar or a structure');
  end  
  if nargin > 6
    net.beta = beta;
  end
end

w = randn(1, net.nwts);
net = rbfunpak(net, w);

% Make widths equal to one
if strcmp(rbfunc, 'gaussian')
  net.wi = ones(1, nhidden);
end

if strcmp(net.outfn, 'neuroscale')
  net.mask = rbfprior(rbfunc, nin, nhidden, nout);
end

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