function model = kperceptr(data,options)% KPERCEPTR Kernel Perceptron.%% Synopsis:%  model = kperceptr(data)%  model = kperceptr(data,options)%% Description:%  This function is an implementation of the kernel version%  of the Perceptron algorithm. The kernel perceptron search %  for the kernel binary classifier with zero emprical error.%% Input:%  data [struct] Binary labeled training data:%   .X [dim x num_data] Vectors.%   .y [1 x num_data] Labels (1 or 2).%  %  options [struct] Control parameters:%   .ker [string] Kernel identifier (default 'linear').%     See 'help kernel' for more info.%   .arg [1 x nargs] Kernel argument.%   .tmax [1x1] Maximal number of iterations (default inf).%% Output:%  model [struct] Found kernel classifer:%   .Alpha [nsv x 1] Multipliers of the training data.%   .b [1x1] Bias of the decision rule.%   .sv.X [dim x nsv] Training data with non-zero Alphas.%   .exitflag [1x1] 1 ... Perceptron has converged.%                   0 ... Maximal number of iterations exceeded.%   .iter [1x1] Number of iterations.%   .kercnt [1x1] Number of kernel evaluations.%   .trnerr [1x1] Training classification error; Note: if exitflag==1 %     then trnerr = 0.%   .options [struct] Copy of options.%   .cputime [real] Used cputime in seconds.%  %  If the linear kernel is used then model.W [dim x 1] contains %  normal vector of the separating hyperplane.%  % Example:%  data = load('vltava');%  model = kperceptr(data, struct('ker','poly','arg',2));%  figure; ppatterns(data); pboundary(model);% % See also SVMCLASS, SVM.%% Modifications: % 10-may-2004, VF% 18-July-2003, VF% 21-Nov-2001, V. Franctic;% process inputs%=======================================if nargin < 2, options=[]; else options=c2s(options); endif ~isfield( options, 'ker'), options.ker = 'linear'; endif ~isfield( options, 'arg'), options.arg = 1; endif ~isfield( options, 'tmax'), options.tmax = inf; end[dim, num_data ] = size( data.X );% change {1,2} --> {1,-1}y = data.y;y(find(y==2)) = -1;% inicialize multiliers Alpha and bias% =========================================Alpha = zeros( num_data,1 );dfce = zeros(num_data,1);  % cache for f(x_i)=<Phi(x_i),w>+bb = 0;exitflag = 0;iter = 0;kercnt = 0;% Main loop%====================================while iter < options.tmax & exitflag == 0,    iter = iter + 1;    [min_dfce, inx ] = min( dfce.*y(:) );    if min_dfce <=0 ,        % Perceptron rule in terms of dot products    old_alpha = Alpha(inx);    old_b = b;    Alpha(inx) = old_alpha + y(inx);    b = old_b + y(inx);        % Updates cache    k_inx = kernel(data.X,data.X(:,inx), options.ker, options.arg );    kercnt = kercnt + num_data;        dfce = dfce + (Alpha(inx)-old_alpha)*k_inx + b - old_b;      else    exitflag = 1;        % scales f(x) such that f(x)=1 for the patterns closest to    % the separating hyperplane    Alpha = Alpha/min_dfce;    b = b/min_dfce;  end  end% fill up structure model%=================================inx = find( Alpha ~= 0);Alpha = Alpha(inx);model.Alpha = Alpha(:);model.b = b;model.sv.X = data.X(:,inx);model.sv.y = data.y(inx);model.sv.inx = inx;model.nsv = length( inx);model.options = options;model.iter = iter;model.kercnt = kercnt;model.trnerr = length( find(dfce.*y(:) < 0))/num_data;model.exitflag = exitflag;model.fun = 'svmclass';if strcmpi('linear',options.ker),  model.W = model.sv.X * model.Alpha;endmodel.cputime = toc;return;