sequential minimal optimization,SMO for SVM, (MATLAB code)

function model = SMOforSVM(X, y, C )
%sequential minimal optimization,SMO

tol = 0.001; maxIters = 3000;

global i1 i2 K Alpha  M1 m1 w b

[m, n] = size(X);

K = (X*X');

Alpha = zeros(m,1); w = 0; b = 0;
flag =1;iters = 1;
while flag >0 & iters < maxIters 
    [i1,i2,m1,M1] = selectWorkSet(y, C);
    if m1 - M1 <= tol
        break;
    end
    solveOptimization(X, y, C)
    iters = iters +1;
end

model.alpha = Alpha;

id = find(Alpha < C & Alpha >0);
% b = mean(y(id)' - (y.*Alpha)'*K(:, id));

id = id(1);
b = y(id)' - (y.*Alpha)'*K(:, id);

w= (y.*Alpha)'* X;
model.w = w;
model.b = b;
end

%Selecting working set B
function [i1,i2,m1,M1]=selectWorkSet(y, C)
global  K Alpha

I_up =find ((Alpha < C & y == 1) | (Alpha > 0 &  y == -1));
I_low = find( (Alpha < C & y == -1) | (Alpha > 0 &  y == 1));
yGradient = - y.* (((y * y').* K) * Alpha - 1);

[m1 , i1] = max(yGradient(I_up)); 
[M1 , i2] = min(yGradient(I_low)); 

i1 = I_up (i1);
i2 = I_low(i2);

end


%Solving the two-variables optimization problem
function solveOptimization(X, y, C)
global Alpha K i1 i2 E
alpha1_old = Alpha(i1);
alpha2_old = Alpha(i2);
y1 = y(i1);
y2 = y(i2);

% x1 = X(i1,:)';
% x2 = X(i2,:)';
beta11 = K(i1,i1); beta22 = K(i2,i2); beta12 = K(i1,i2);
id  =[1: length(Alpha)];
id([i1 i2]) = [];
beta1 = sum( y(id).*Alpha(id).*K(id,i1));
beta2 = sum( y(id).*Alpha(id).*K(id,i2));

E = beta1 - beta2 + alpha1_old * y1 * (beta11 - beta12) +alpha2_old*y2 * (beta12 - beta22) - y1 + y2;
kk = beta11 + beta22 - 2 * beta12;
alpha2_new_unc = alpha2_old + (y2 * E)/kk;

if y1 ~= y2
    L = max([0 , alpha2_old - alpha1_old]);
    H = min([C, C - alpha1_old + alpha2_old]);
else
    L = max([0 , alpha1_old + alpha2_old - C]);
    H = min([C,  alpha1_old + alpha2_old]);
end

if  alpha2_new_unc > H
    alpha2_new = H;
elseif  alpha2_new_unc < L
    alpha2_new = L;
else
    alpha2_new = alpha2_new_unc ;
end

alpha1_new =  alpha1_old + y1 * y2 * (alpha2_old - alpha2_new);

Alpha(i1) = alpha1_new;
Alpha(i2) = alpha2_new;

% for i=1:length(E)
%     E(i) = sum(y .* Alphas .* K(i,:)) - b - y(i);
% end
% 
% 
% E1 = E(i1);
% E2 = E(i2);
% 
% b1 = E1 + y1 * (a1 - alph1) * K(i1,i1) + y2 * (a2 - alph2) * K(i1,i2) - b;
% b2 = E2 + y1 * (a1 - alph1) * K(i1,i2) + y2 * (a2 - alph2) * K(i2,i2) - b;
% 
% if b1 == b2
%     b = b1;
% else
%     b = mean([b1 b2]);
% end

% w = w - y1 * (alpha1_new -alpha1_old) * X(i1,:)' - y2 * (alpha2_new -alpha2_old) * X(i2,:)';

end

　　

clear
X = []; Y=[];
figure;
% Initialize training data to empty; will get points from user
% Obtain points froom the user:
trainPoints=X;
trainLabels=Y;
clf;
axis([-5 5 -5 5]);
if isempty(trainPoints)
    % Define the symbols and colors we'll use in the plots later
    symbols = {'o','x'};
    classvals = [-1 1];
    trainLabels=[];
    hold on; % Allow for overwriting existing plots
    xlim([-5 5]); ylim([-5 5]);
    
    for c = 1:2
        title(sprintf('Click to create points from class %d. Press enter when finished.', c));
        [x, y] = getpts;
        
        plot(x,y,symbols{c},'LineWidth', 2, 'Color', 'black');
        
        % Grow the data and label matrices
        trainPoints = vertcat(trainPoints, [x y]);
        trainLabels = vertcat(trainLabels, repmat(classvals(c), numel(x), 1));        
    end

end


C = 10;
par = SMOforSVM(trainPoints, trainLabels , C );
p=length(par.b); m=size(trainPoints,2);
 if m==2
%     for i=1:p
%         plot(X(lc(i)-l(i)+1:lc(i),1),X(lc(i)-l(i)+1:lc(i),2),'bo')
%         hold on
%     end
    k = -par.w(1)/par.w(2);
    b0 = - par.b/par.w(2);
    bdown=(-par.b-1)/par.w(2);
    bup=(-par.b+1)/par.w(2);
    for i=1:p
        hold on
        h = refline(k,b0(i)); 
        set(h, 'Color', 'r') 
        hdown=refline(k,bdown(i));
        set(hdown, 'Color', 'b') 
        hup=refline(k,bup(i));
        set(hup, 'Color', 'b') 
    end  
 end
xlim([-5 5]); ylim([-5 5]);

 以上代码结果写的比较粗糙，可能不稳定，我重新贴了一个新的代码：

http://www.cnblogs.com/huadongw/p/4994657.html