SMO推导和代码-记录毕业论文4

SMO的数学公式通过Platt的论文和看这个博客：http://www.cnblogs.com/jerrylead/archive/2011/03/18/1988419.html，大概弄懂了。推导以后再写，贴上一个自己写的SMO的代码。

function [ model ] = smoSolver( designMatrix, targetGroup )numChanged = 0;examineAll = 1;tolerance = 0.001; total_runtimes = 5000; epsilon = 0.01;n_samps = size(designMatrix,1);kernelMatrix = zeros(n_samps, n_samps);for i = 1 : n_samps    for j = i : n_samps        kernelMatrix(i,j) = dot(designMatrix(i,:), designMatrix(j,:));        kernelMatrix(j,i) =  kernelMatrix(i,j);    endendalphaArray = rand(1, n_samps);C = 1; b = 0;u = alphaArray .* targetGroup * kernelMatrix - b;E = u - targetGroup;iter = 1 ;while(numChanged > 0 || examineAll)    numChanged = 0;    if(examineAll)        for i = 1 : n_samps            numChanged = numChanged + examineExample(i);        end    else        for i = 1 : n_samps            if abs(alphaArray(i)) > tolerance && abs(alphaArray(i)-C) > tolerance                numChanged = numChanged + examineExample(i);            end        end    end    if(examineAll == 1)        examineAll = 0;    elseif (numChanged == 0)        examineAll = 1;    end    iter = iter + 1;    if iter > total_runtimes        break;    endendfunction changed = examineExample(i)    y2 = targetGroup(i);    alpha2 = alphaArray(i);    E2 = E(i);    r2 = E2 * y2;    %if((r2 < -0.01 && alpha2 < C) || (r2 > 0.01 && alpha2 > 0))    if( (r2 < -tolerance && abs(alpha2) < tolerance) || ...         (r2 > tolerance && abs(alpha2-C) < tolerance) || ...         (abs(r2) > tolerance && alpha2 < C-tolerance && alpha2 > tolerance ) )        non_zero_non_c = find(abs(alphaArray)>0.01 & abs(alphaArray-C)>0.01);        if length(non_zero_non_c) > 1            maxIdx = 1; max = 0;            for idx = 1 : n_samps                if abs(E(idx) - E2) > max                    max = abs(E(idx) - E2);                    maxIdx = idx;                end            end            if takeStep(maxIdx, i)                changed = 1; return;            end        end                for k = 1 : length(non_zero_non_c)            i1 = non_zero_non_c(k);            if takeStep(i1, i);                changed = 1; return;            end        end                for k = 1 : n_samps            if takeStep(k, i)                changed = 1; return;            end        end    end    changed = 0; return;endfunction tf = takeStep(i1, i2)if i1 == i2    tf = 0; return;endalpha1 = alphaArray(i1); a1 = 0;alpha2 = alphaArray(i2); a2 = 0;y1 = targetGroup(i1); y2 = targetGroup(i2);E1 = E(i1); E2 = E(i2);s = y1 * y2;if s > 0    L = max([0,alpha1+alpha2-C]);    H = min([C,alpha1+alpha2]);else    L = max([0,alpha2-alpha1]);    H = min([C, C+alpha2-alpha1]);endif L == H    tf = 0; return;endk11 = kernelMatrix(i1,i1);k12 = kernelMatrix(i1,i2);k22 = kernelMatrix(i2,i2);eta = k11 + k22 - 2*k12;if(eta > 0)    a2 = alpha2 + y2 * (E1-E2)/eta;     if(a2 < L)         a2 = L;    elseif (a2 > H)        a2 = H;    endelse    a2 = L;    a1 = alpha1 + s*(alpha2-a2);    alphaArrayTmp = alphaArray; alphaArrayTmp(i1) = a1; alphaArrayTmp(i2) = a2;    alphaArrayTmp = alphaArrayTmp .* targetGroup;    Lobj = 0.5 * alphaArrayTmp * kernelMatrix * alphaArrayTmp' - sum(alphaArrayTmp);        a2 = H;    a1 = alpha1 + s*(alpha2-a2);    alphaArrayTmp = alphaArray; alphaArrayTmp(i1) = a1; alphaArrayTmp(i2) = a2;    alphaArrayTmp = alphaArrayTmp .* targetGroup;    Hobj = 0.5 * alphaArrayTmp * kernelMatrix * alphaArrayTmp' - sum(alphaArrayTmp);    if(Lobj < Hobj - epsilon)        a2 = L;    elseif(Lobj > Hobj + epsilon)        a2 = H;    else        a2 = alpha2;    endendif (abs(a2-alpha2) < 0.01*(a2+alpha2+epsilon))    tf = 0; return;enda1 = alpha1 + s*(alpha2-a2);b1 = E1 + y1*(a1 - alpha1)*kernelMatrix(i1,i1)+y2*(a2 - alpha2)*kernelMatrix(i1,i2)+b;b2 = E2 + y1*(a1 - alpha1)*kernelMatrix(i1,i2)+y2*(a2 - alpha2)*kernelMatrix(i2,i2)+b;if(a1 > 0 && a1 < C)    b = b1;elseif(a2 > 0 && a2 < C)    b = b2;else    b = (b1+b2)/2;endalphaArray(i1) = a1; alphaArray(i2) = a2;u = alphaArray .* targetGroup * kernelMatrix - b;E = u - targetGroup;tf = 1; return;endu = alphaArray .* targetGroup * kernelMatrix - b;alphaIdx = find(abs(alphaArray) > tolerance); model.targetGroup = targetGroup(alphaIdx);model.alpha = alphaArray(alphaIdx);model.supVec = designMatrix(alphaIdx, :);model.b = b;end

smoPredict:

function [ targetGroup ] = smoPredict( model, designMatrix )kernelMatrix = model.supVec * designMatrix';u = sum(kernelMatrix' .* model.alpha .* model.targetGroup) - model.b;targetGroup = sign(u);end