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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]);
sequential minimal optimization,SMO for SVM, (MATLAB code)
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原文地址：http://www.cnblogs.com/huadongw/p/4601377.html
