%perceptron.m - perceptron learning algorithm% INput: train(:,1:M) - pattern  train(:,M+1) - target% Output: weight vector w=[w0 w1 ... wM], w0: bias%     actual output vector y% Need to call m-file routine: datasepf.m, sline.m% copyright (C) 1996-2001 by Yu Hen Hu% Modified: 2/9/2000, 2/3/2001% K2: # of training samples% M: feature space dimensionclear all, clfgdata=input('Enter 0 to load a data file, Return to generate separable data: ');if isempty(gdata)|gdata~=0,   % generate random training data   K2=input('number of training samples = ');   [orig,slope]=datasepf(K2);   % slope is the slope of separating plane   % that has the formula:  y = slope*x + 0.5*(1-slope)else   disp('enter the data matrix, row by row, [x1 .. xN t]');	orig=input(' start from class 1, followed by class 0: ');end[Km,Kn]=size(orig);M=Kn-1;  % number of inputsK0=sum([orig(:,Kn)==0]);  K1=Km-K0;  K2=K0+K1;% # of targets = 0 and 1 mdisplay=10; % # of displaying hyperplane before checking for stopping % Initial hyperplane% w=[rand(1,M) 0];  % initial random weights% The initial hyperplane can be estimated as a hyperplane separating% a pair of data sample with different labels% in orig, this is the first and the last data sample since there are% only two classes and sorted according to class labels% the separating hyperplane of two points a and b % has the normal vector  [-0.5(|b|^2-|a|^2) b-a]wa=orig(1,1:M); wb=orig(K2,1:M);wmag=0.5*(wb*wb'-wa*wa');wunit=wb-wa;w=[-wmag wunit(1) wunit(2)];figure(1)subplot(1,2,2),plot(orig(1:K1,1),orig(1:K1,2),'*',orig(K1+1:K2,1),orig(K1+1:K2,2),'o')axis('square');v=axis;[lx,ly]=sline(w,v);subplot(1,2,1),plot(orig(1:K1,1),orig(1:K1,2),'*',...   orig(K1+1:K2,1),orig(K1+1:K2,2),'o',lx,ly)axis('square');title('Initial hyperplane')converged=0;% 0 < eta < 1/x(k)_max.etamax=sqrt(max(orig(:,1).*orig(:,1)+orig(:,2).*orig(:,2)));eta=input(['0 < eta < ' num2str(etamax) ', Enter eta = '])epoch=0;while converged==0, % not converged yet   train=randomize(orig);   for i=1:K2,     y(i)=0.5*(1+sign(w*[1;train(i,1:M)']));     w=w+eta*(train(i,M+1)-y(i))*[1 train(i,1:M)];     [lx,ly]=sline(w,v);     subplot(1,2,2),plot(orig(1:K1,1),orig(1:K1,2),'*g',...        orig(K1+1:K2,1),orig(K1+1:K2,2),'og',lx,ly,'-',...        train(i,1),train(i,2),'sr');     axis('square');     pause(0.1)     drawnow   end % for loop   epoch=epoch+1;   if sum(abs(train(:,M+1)-y'))==0, % check if converged      converged=1;   end   if rem(epoch,mdisplay)==0,      converged=input('type 1 to terminate, Return to continue : ')      if isempty(converged),          converged=0;      end   end   if converged==1,      [lx,ly]=sline(w,v);      subplot(1,2,2),plot(orig(1:K1,1),orig(1:K1,2),'*',...         orig(K1+1:K2,1),orig(K1+1:K2,2),'o',lx,ly)      axis('square');      title('final hyperplane location')   endend % while loop