wolffd@0: function net = rbf(nin, nhidden, nout, rbfunc, outfunc, prior, beta)
wolffd@0: %RBF	Creates an RBF network with specified architecture
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	NET = RBF(NIN, NHIDDEN, NOUT, RBFUNC) constructs and initialises a
wolffd@0: %	radial basis function network returning a data structure NET. The
wolffd@0: %	weights are all initialised with a zero mean, unit variance normal
wolffd@0: %	distribution, with the exception of the variances, which are set to
wolffd@0: %	one. This makes use of the Matlab function RANDN and so the seed for
wolffd@0: %	the random weight initialization can be  set using RANDN('STATE', S)
wolffd@0: %	where S is the seed value. The activation functions are defined in
wolffd@0: %	terms of the distance between the data point and the corresponding
wolffd@0: %	centre.  Note that the functions are computed to a convenient
wolffd@0: %	constant multiple: for example, the Gaussian is not normalised.
wolffd@0: %	(Normalisation is not needed as the function outputs are linearly
wolffd@0: %	combined in the next layer.)
wolffd@0: %
wolffd@0: %	The fields in NET are
wolffd@0: %	  type = 'rbf'
wolffd@0: %	  nin = number of inputs
wolffd@0: %	  nhidden = number of hidden units
wolffd@0: %	  nout = number of outputs
wolffd@0: %	  nwts = total number of weights and biases
wolffd@0: %	  actfn = string defining hidden unit activation function:
wolffd@0: %	    'gaussian' for a radially symmetric Gaussian function.
wolffd@0: %	    'tps' for r^2 log r, the thin plate spline function.
wolffd@0: %	    'r4logr' for r^4 log r.
wolffd@0: %	  outfn = string defining output error function:
wolffd@0: %	    'linear' for linear outputs (default) and SoS error.
wolffd@0: %	    'neuroscale' for Sammon stress measure.
wolffd@0: %	  c = centres
wolffd@0: %	  wi = squared widths (null for rlogr and tps)
wolffd@0: %	  w2 = second layer weight matrix
wolffd@0: %	  b2 = second layer bias vector
wolffd@0: %
wolffd@0: %	NET = RBF(NIN, NHIDDEN, NOUT, RBFUND, OUTFUNC) allows the user to
wolffd@0: %	specify the type of error function to be used.  The field OUTFN is
wolffd@0: %	set to the value of this string.  Linear outputs (for regression
wolffd@0: %	problems) and Neuroscale outputs (for topographic mappings) are
wolffd@0: %	supported.
wolffd@0: %
wolffd@0: %	NET = RBF(NIN, NHIDDEN, NOUT, RBFUNC, OUTFUNC, PRIOR, BETA), in which
wolffd@0: %	PRIOR is a scalar, allows the field NET.ALPHA in the data structure
wolffd@0: %	NET to be set, corresponding to a zero-mean isotropic Gaussian prior
wolffd@0: %	with inverse variance with value PRIOR. Alternatively, PRIOR can
wolffd@0: %	consist of a data structure with fields ALPHA and INDEX, allowing
wolffd@0: %	individual Gaussian priors to be set over groups of weights in the
wolffd@0: %	network. Here ALPHA is a column vector in which each element
wolffd@0: %	corresponds to a separate group of weights, which need not be
wolffd@0: %	mutually exclusive.  The membership of the groups is defined by the
wolffd@0: %	matrix INDX in which the columns correspond to the elements of ALPHA.
wolffd@0: %	Each column has one element for each weight in the matrix, in the
wolffd@0: %	order defined by the function RBFPAK, and each element is 1 or 0
wolffd@0: %	according to whether the weight is a member of the corresponding
wolffd@0: %	group or not. A utility function RBFPRIOR is provided to help in
wolffd@0: %	setting up the PRIOR data structure.
wolffd@0: %
wolffd@0: %	NET = RBF(NIN, NHIDDEN, NOUT, FUNC, PRIOR, BETA) also sets the
wolffd@0: %	additional field NET.BETA in the data structure NET, where beta
wolffd@0: %	corresponds to the inverse noise variance.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	RBFERR, RBFFWD, RBFGRAD, RBFPAK, RBFTRAIN, RBFUNPAK
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: net.type = 'rbf';
wolffd@0: net.nin = nin;
wolffd@0: net.nhidden = nhidden;
wolffd@0: net.nout = nout;
wolffd@0: 
wolffd@0: % Check that function is an allowed type
wolffd@0: actfns = {'gaussian', 'tps', 'r4logr'};
wolffd@0: outfns = {'linear', 'neuroscale'};
wolffd@0: if (strcmp(rbfunc, actfns)) == 0
wolffd@0:   error('Undefined activation function.')
wolffd@0: else
wolffd@0:   net.actfn = rbfunc;
wolffd@0: end
wolffd@0: if nargin <= 4
wolffd@0:    net.outfn = outfns{1};
wolffd@0: elseif (strcmp(outfunc, outfns) == 0)
wolffd@0:    error('Undefined output function.')
wolffd@0: else
wolffd@0:    net.outfn = outfunc;
wolffd@0:  end
wolffd@0: 
wolffd@0: % Assume each function has a centre and a single width parameter, and that
wolffd@0: % hidden layer to output weights include a bias.  Only the Gaussian function
wolffd@0: % requires a width
wolffd@0: net.nwts = nin*nhidden + (nhidden + 1)*nout;
wolffd@0: if strcmp(rbfunc, 'gaussian')
wolffd@0:   % Extra weights for width parameters
wolffd@0:   net.nwts = net.nwts + nhidden;
wolffd@0: end
wolffd@0: 
wolffd@0: if nargin > 5
wolffd@0:   if isstruct(prior)
wolffd@0:     net.alpha = prior.alpha;
wolffd@0:     net.index = prior.index;
wolffd@0:   elseif size(prior) == [1 1]
wolffd@0:     net.alpha = prior;
wolffd@0:   else
wolffd@0:     error('prior must be a scalar or a structure');
wolffd@0:   end  
wolffd@0:   if nargin > 6
wolffd@0:     net.beta = beta;
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: w = randn(1, net.nwts);
wolffd@0: net = rbfunpak(net, w);
wolffd@0: 
wolffd@0: % Make widths equal to one
wolffd@0: if strcmp(rbfunc, 'gaussian')
wolffd@0:   net.wi = ones(1, nhidden);
wolffd@0: end
wolffd@0: 
wolffd@0: if strcmp(net.outfn, 'neuroscale')
wolffd@0:   net.mask = rbfprior(rbfunc, nin, nhidden, nout);
wolffd@0: end
wolffd@0: