% PERLC - Train a linear perceptron classifier% %   W = PERLC(A)%   W = PERLC(A,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). %% SEE ALSO% DATASETS, MAPPINGS, NMC, FISHERC, BPXNC, LMNC% Copyright: D. de Ridder, R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Sciences, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: perlc.m,v 1.9 2006/03/07 16:15:54 duin Exp $function w = perlc (a, maxiter, eta, w_ini, type)	prtrace(mfilename);    if (nargin  < 5 | isempty(type))    type = 'batch';  end	if (nargin < 4 | isempty(w_ini))		prwarning(3,'No initial weights W_INI supplied, using random initialization');		w_ini = []; 	end	if (nargin < 3 | isempty(eta))		prwarning(3,'Learning rate ETA not specified, assuming 0.1');		eta = 0.1;     	end	if (nargin < 2 | isempty(maxiter))		prwarning(3,'Maximum number of iterations not specified, assuming 100');		maxiter = 100; 	end	if (nargin < 1) | (isempty(a))		w = mapping(mfilename,{maxiter,eta,w_ini});		w = setname(w,'Linear Perceptron');		return	end  		% Unpack the dataset.	islabtype(a,'crisp');	isvaldset(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;		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);    end		% Build the classifier		w = ws*affine(weights(1:k,:),weights(k+1,:),a);		w = cnormc(w,a);		else   % multi-class classifier:				w = mclassc(a,mapping(mfilename,{maxiter,eta,w_ini}));			end			return