function model=perceptron(data,options,init_model)% PERCEPTRON Perceptron algorithm to train binary linear classifier. %% Synopsis:%  model = perceptron(data)%  model = perceptron(data,options)%  model = perceptron(data,options,init_model)%% Description:%  model = perceptron(data) uses the Perceptron learning rule%   to find separating hyperplane from given binary labeled data.%%  model = perceptron(data,options) specifies stopping condition of%   the algorithm in structure options:%    .tmax [1x1]... maximal number of iterations.%%   If tmax==-1 then it only returns index (model.last_update)%   of data vector which should be used by the algorithm for updating%   the linear rule in the next iteration.%%  model = perceptron(data,options,init_model) specifies initial model%   which must contain:%    .W [dim x 1] ... normal vector.%    .b [1x1] ... bias of hyperplane.%    .t [1x1] (optional) ... iteration number.%% Input:%  data [struct] Labeled (binary) training data. %   .X [dim x num_data] Input vectors.%   .y [1 x num_data] Labels (1 or 2).%%  options [struct] %   .tmax [1x1] Maximal number of iterations (default tmax=inf).%     If tmax==-1 then it does not perform any iteration but returns only %     index of the point which should be used to update linear rule.%  %  init_model [struct] Initial model; must contain items%    .W, .b and .t (see above).%% Output:%  model [struct] Binary linear classifier:%   .W [dim x 1] Normal vector of hyperplane.%   .b [1x1] Bias of hyperplane.%  %   .exitflag [1x1] 1 ... perceptron has converged.%                   0 ... number of iterations exceeded tmax.%   .t [int] Number of iterations.%   .last_update [d x 1] Index of the last point used for update.%% Example:%  data = genlsdata( 2, 50, 1);%  model = perceptron(data)%  figure; ppatterns(data); pline(model); %% See also %  EKOZINEC, MPERCEPTRON, LINCLASS.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 17-sep-2003, VF% 16-Feb-2003, VF% 20-Jan-2003, VF% 7-jan-2002, VF. A new coat.% 24. 6.00 V. Hlavac, comments polished.% 15-dec-2000, texts, returns bad point% get data dimensions[dim,num_data] = size(data.X);% Process input arguments % -----------------------------if nargin < 2, options = []; else options = c2s(options); endif ~isfield(options,'tmax'), options.tmax = inf; endif nargin < 3,  % create init model  %----------------------------  model.W = zeros(dim,1);  model.b = 0;else  % take init model from input  %----------------------------  model = init_model;endif ~isfield(model,'t'), model.t = 0; endmodel.exitflag = 0;model.last_update = 0;% Add one constant coordinates to the data and swap% points from the second class along the origin.% ----------------------------------------------------data.X = [data.X; ones(1,num_data)];dim=dim+1;inx = find(data.y==2);data.X(:,inx) = -data.X(:,inx);W = [model.W;model.b];                                                         if options.tmax == -1,  % return index of point which should be used to update linear rule  %----------------------------------------------------------------------  fvalue = data.X'*W;  inx = find( fvalue <= 0 );    if length(inx)==0,    model.exitflag = 1;  else    model.exitflag = 0;    model.last_update = inx(1);  endelse  % main loop   % -----------------------------------  while options.tmax > model.t & model.exitflag == 0,    model.t = model.t+1;        % Compute discriminant function for all data    fvalue = data.X'*W;    inx = find( fvalue <= 0 );      if length(inx)==0,      model.exitflag = 1;    else      inx = inx(1);      model.exitflag = 0;      model.last_update = inx;      % Update model using the Perceptron rule      W = W + data.X(:,inx);    end  end     % separates normal vector and bias  model.W = W(1:dim-1);  model.b = W(dim);endmodel.fun = 'linclass';return;