%RBNC Trainable radial basis neural network classifier
%
% W = RBNC(A,UNITS)
% W = A*RBNC([],UNITS)
% W = A*RBNC(UNITS)
%
% INPUT
% A Dataset
% UNITS Number of RBF units in hidden layer
%
% OUTPUT
% W Radial basis neural network mapping
%
% DESCRIPTION
% A feed-forward neural network classifier with one hidden layer with
% UNITS radial basis units is computed for labeled dataset A.
% Default UNITS is number of objects * 0.2, but not more than 100.
% Uses the Mathworks' Neural Network toolbox.
%
% If UNITS is NaN it is optimised by REGOPTC. This may take a long
% computing time and is often not significantly better than the default.
%
% This routine calls MathWork's SOLVERB routine (Neural Network toolbox)
% as SOLVB.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, LMNC, BPXNC, NEURC, RNNC, REGOPTC
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: rbnc.m,v 1.4 2007/06/19 11:45:08 duin Exp $
function w = rbnc(varargin)
checktoolbox('nnet');
mapname = 'RB-NeuralNet';
argin = shiftargin(varargin,'integer');
argin = setdefaults(argin,[],[]);
if mapping_task(argin,'definition')
w = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a,units] = deal(argin{:});
if isnan(units) % optimize complexity parameter: number of neurons
defs = {[]};
parmin_max = [1,30];
w = regoptc(a,mfilename,{units},defs,[1],parmin_max,testc([],'soft'),0);
return
end
if isempty(units)
units = min(ceil(size(a,1)/5),100);
end
if units > size(a,1)
error('Number of hidden units should not increase datasize')
end
% Training target values.
target_low = 0.1;
target_high = 0.9;
islabtype(a,'crisp');
isvaldfile(a,2,2); % at least 2 objects per class, 2 classes
a = testdatasize(a);
[m,k,c] = getsize(a); nlab = getnlab(a);
% Set standard training parameters.
disp_freq = inf; % Display interval: switch off
err_goal = 0.005*m; % Sum squared error goal, stop if reached
sigma = 0.5; % RBF kernel width
% Create target matrix: row C contains a high value at position C,
% the correct class, and a low one for the incorrect ones (place coding).
target = target_low * ones(c,c) + (target_high - target_low) * eye(c);
target = target(nlab,:)';
% Shift and scale the training set to zero mean, unit variance.
ws = scalem(a,'variance');
% Add noise to training set, as SOLVB sometimes has problems with
% identical inputs.
r = randn(m,k) * 1e-6;
% Compute RBF network.
% RD I changed the below call from NEWRBE() to NEWRB() and added
% the number of units as parameter. NEWRBE always uses M units
% net = newrb(+(a*ws)'+r',target,sigma);
if verLessThan('nnet','7.0')
net = newrb(+(a*ws)'+r',target,0,sigma,units,inf);
else
% we need a debugged version of pr_newrb
net = pr_newrb(+(a*ws)'+r',target,0,sigma,units,inf);
end
weight1 = net.IW{1,1}; weight2 = net.LW{2,1};
bias1 = net.b{1}; bias2 = net.b{2};
n_hidden_units = length(bias1);
% Construct resulting map. First apply the shift and scale mapping WS.
% The first layer then calculates EXP(-D), where D are the squared
% distances to RBF kernel centers, scaled by the biases.
w = ws*proxm(weight1,'distance',2); % RBF distance map
w = w*cmapm(bias1'.^(-2),'scale'); % Multiply by scale (sq. bias)
w = w*cmapm(n_hidden_units,'nexp'); % Take negative exponential
% Second layer is affine mapping on output of first layer, followed
% by a sigmoid mapping.
%w = nodatafile*w*affine(weight2',bias2',[],getlablist(a))*sigm;
w = nodatafile*w*affine(weight2',bias2',[],getlablist(a));
w = setout_conv(w,1); % takes care of sigm and makes it a classifier
w = setname(w,mapname);
end