% PERLC - Trainable linear perceptron classifier
%
% W = PERLC(A,MAXITER,ETA,W_INI,TYPE)
% W = A*PERLC([],MAXITER,ETA,W_INI,TYPE)
% W = A*PERLC(MAXITER,ETA,W_INI,TYPE)
%
% INPUT
% A Training dataset
% MAXITER Maximum number of iterations (default 100)
% ETA Learning rate (default 0.1)
% W_INI Initial weights, as affine mapping, e.g W_INI = NMC(A)
% (default: random initialisation)
% TYPE 'batch': update by batch processing (default)
% 'seq' : update sequentially
%
% OUTPUT
% W Linear perceptron classifier mapping
%
% DESCRIPTION
% Outputs a perceptron W trained on dataset A using learning rate ETA for a
% maximum of MAXITER iterations (or until convergence).
%
% If ETA is NaN it is optimised by REGOPTC.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, NMC, FISHERC, BPXNC, LMNC, REGOPTC
% Copyright: D. de Ridder, 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
function w = perlc (varargin)
mapname = 'Perceptron';
argin = shiftargin(varargin,'scalar');
argin = setdefaults(argin,[],100,0.1,[],'batch');
if mapping_task(argin,'definition')
w = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a, maxiter, eta, w_ini, type] = deal(argin{:});
if isnan(eta) % optimize regularisation parameter
defs = {100,0.1,[],'batch'};
parmin_max = [0,0;1e-6,0.9;0,0;0,0];
w = regoptc(a,mfilename,{maxiter, eta, w_ini, type},defs,[2],parmin_max,testc([],'soft'),1);
return
end
% Unpack the dataset.
islabtype(a,'crisp');
isvaldfile(a,1,2); % at least 1 object per class, 2 classes
[m,k,c] = getsize(a);
nlab = getnlab(a);
% PERLC is basically a 2-class classifier. More classes are
% handled by mclassc.
if c == 2 % two-class classifier
ws = scalem(a,'variance');
a = a*ws;
% Add a column of 1's for the bias term.
Y = [+a ones(m,1)];
% Initialise the WEIGHTS with a small random uniform distribution,
% or with the specified affine mapping.
if isempty(w_ini)
weights = 0.02*(rand(k+1,c)-0.5);
else
isaffine(w_ini);
weights = [w_ini.data.rot;w_ini.data.offset];
end
converged = 0; iter = 0;
s = sprintf('perlc, %i iterations: ',maxiter);
prwaitbar(maxiter,s,m*k>100000);
while (~converged)
% Find the maximum output for each sample.
[maxw,ind] = max((Y*weights)');
changed = 0;
if (strcmp(type,'batch'))
% Update for all incorrectly classified samples simultaneously.
changed = 0;
for i = 1:m
if (ind(i) ~= nlab(i))
weights(:,nlab(i)) = weights(:,nlab(i)) + eta*Y(i,:)';
weights(:,ind(i)) = weights(:,ind(i)) - eta*Y(i,:)';
changed = 1;
end;
end;
iter = iter+1;
else
% update for the worst classified object only
J = find(ind' ~= nlab);
if ~isempty(J)
[dummy,imax] = min(maxw(J)); i = J(imax);
weights(:,nlab(i)) = weights(:,nlab(i)) + eta*Y(i,:)';
weights(:,ind(i)) = weights(:,ind(i)) - eta*Y(i,:)';
iter = iter+1;
changed = 1;
end;
end
% Continue until things stay the same or until MAXITER iterations.
converged = (~changed | iter >= maxiter);
prwaitbar(maxiter,iter,[s int2str(iter)]);
end
prwaitbar(0);
% Build the classifier
w = ws*affine(weights(1:k,:),weights(k+1,:),a);
w = cnormc(w,a);
w = setlabels(w,getlablist(a));
w = setname(w,mapname);
else % multi-class classifier:
w = mclassc(a,prmapping(mfilename,{maxiter,eta,w_ini}));
w = setname(w,mapname);
end
end
return