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