function model = smo( data, options, init_model)% SMO Sequential Minimal Optimization for binary SVM with L1-soft margin.%% Synopsis:%  model = smo( data )%  model = smo( data, options )%  model = smo( data, options, init_model)%% Description:%  This function is implementation of the Sequential Minimal %  Optimizer (SMO) [Platt98] to train the binary Support Vector %  Machines Classifier with L1-soft margin.%           % Input:%  data [struct] Binary labeled training vectors:%   .X [dim x num_data] Training vectors.%   .y [a 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(s) (default 1).%   .C Regularization constant (default C=inf). The constant C can %     be given as:%      C [1x1] .. for all data.%      C [1x2] .. for each class separately C=[C1,C2].%      C [1xnum_data] .. for each training vector separately.%   .eps [1x1] SMO paramater (default 0.001).%   .tol [1x1] Tolerance of KKT-conditions (default 0.001).%  %  init_model [struct] Specifies initial model:%   .Alpha [num_data x 1] Initial model. %   .b [1x1] Bias.%  If not given then it is set to zero by default.%% Output:%  model [struct] Binary SVM classifier:%   .Alpha [nsv x 1] Weights (Lagrangians).%   .b [1x1] Bias.%   .sv.X [dim x nsv] Support vectors.%   .nsv [1x1] Number of Support Vectors.%   .kercnt [1x1] Number of kernel evaluations used by SMO.%   .trnerr [1x1] Training classification error.%   .margin [1x1] Margin of the found classifier.%   .cputime [1x1] Used CPU time in seconds.%   .options [struct] Copy of used options.%% Example:%  trn = load('riply_trn');  %  model = smo(trn,struct('ker','rbf','C',10,'arg',1));%  figure; ppatterns(trn); psvm(model); %  tst = load('riply_tst');%  ypred = svmclass( tst.X, model );%  cerror( ypred, tst.y )%% See also %  SVMCLASS, SVMLIGHT, SVMQUADPROG.%% 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:% 23-may-2004, VF% 17-September-2001, V. Franc, created% timertic;% Input arguments %-------------------------------------------------------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,'C'), options.C = inf; endif ~isfield(options,'eps'), options.eps = 0.001; endif ~isfield(options,'tol'), options.tol = 0.001; end[dim,num_data] = size(data.X);if nargin < 3,  init_model.Alpha = zeros(num_data,1);   init_model.b = 0;end% run optimizer%----------------------------------------------------[model.Alpha, model.b, model.nsv, model.kercnt, model.trnerr, model.margin]...   = smo_mex(data.X, data.y, options.ker, options.arg, options.C, ...     options.eps, options.tol, init_model.Alpha, init_model.b );% set up output%------------------------------------------------------inx = find( model.Alpha );model.sv.X = data.X(:,inx);model.sv.y = data.y(inx);model.sv.inx = inx;model.Alpha = model.Alpha(inx);model.Alpha(find(model.sv.y == 2)) = -model.Alpha(find(model.sv.y == 2));% computes normal vector of the hypeprlane if linear kernel usedif strcmpi(options.ker,'linear'),  model.W = model.sv.X*model.Alpha;endmodel.options = options;model.fun = 'svmclass';model.cputime = toc;return;