determine_alpha2.m

核方法＆svm是模式识别是很重要的方法

function [ alpha2,alpha2_index,alpha2_new ] = determine_alpha2( mat_kernel,E,alpha,Y,littleValue,C,alpha1,alpha1_index)
%UNTITLED1 Summary of this function goes here
%  Detailed explanation goes here

%determine alpha2 by minimizing E1-E2
E1 = E(alpha1_index);
E1_E2 = max(abs(E-E1));
alpha2_index_s = find(abs(E-E1)==E1_E2);
alpha2_s = alpha(alpha2_index_s);
for i=1:length(alpha2_s)
    alpha2_index =alpha2_index_s(i);
    alpha2 = alpha2_s(i);
    if(Y(alpha1_index,1) ~= Y(alpha2_index,1))
        U = max(0,alpha2-alpha1);
        V = min(C,C-alpha1+alpha2);
    else
        U = max(0,alpha1+alpha2-C);
        V = min(C,alpha1+alpha2);
    end

    k = mat_kernel(alpha1_index,alpha1_index)+mat_kernel(alpha2_index,alpha2_index)-2*mat_kernel(alpha1_index,alpha2_index);
    if abs(k)<littleValue
        continue;
    end
    alpha2_new = alpha2+Y(alpha2_index,1)*(E1-E(alpha2_index,1))/k;
    if alpha2_new > V
        alpha2_new = V;
    elseif alpha2_new < U
        alpha2_new = U;
    end
    if abs(alpha2_new-alpha2) < littleValue
        continue
    else
        break
    end
end

%determine alpha2 from support vector
if abs(alpha2_new-alpha2) < littleValue
    sup_index = find(alpha>littleValue & alpha<C-littleValue);
    if ~isempty(sup_index)
        for j = 1:length(sup_index)
            alpha2_index = sup_index(j);
            alpha2 = alpha(alpha2_index);
            if(Y(alpha1_index,1) ~= Y(alpha2_index,1))
                U = max(0,alpha2-alpha1);
                V = min(C,C-alpha1+alpha2);
            else
                U = max(0,alpha1+alpha2-C);
                V = min(C,alpha1+alpha2);
            end

            k = mat_kernel(alpha1_index,alpha1_index)+mat_kernel(alpha2_index,alpha2_index)-2*mat_kernel(alpha1_index,alpha2_index);
            if abs(k)<littleValue
                continue;
            end
            alpha2_new = alpha2_new+Y(alpha2_index,1)*(E(alpha2_index,1)-E1)/k;
            if alpha2_new > V
                alpha2_new = V;
            elseif alpha2_new < U
                alpha2_new = U;
            end
            if abs(alpha2_new-alpha2) < littleValue
                continue
            else
                break
            end
        end
    end
end

%determine alpha2 from all training samples
if abs(alpha2_new-alpha2) < littleValue
    clear i;
    for i = 1:length(alpha)
        alpha2_index = i;
        alpha2 = alpha(alpha2_index);
        if(Y(alpha1_index,1) ~= Y(alpha2_index,1))
            U = max(0,alpha2-alpha1);
            V = min(C,C-alpha1+alpha2);
        else
            U = max(0,alpha1+alpha2-C);
            V = min(C,alpha1+alpha2);
        end

        k = mat_kernel(alpha1_index,alpha1_index)+mat_kernel(alpha2_index,alpha2_index)-2*mat_kernel(alpha1_index,alpha2_index);
        if abs(k)<littleValue
            continue;
        end
        alpha2_new = alpha2_new+Y(alpha2_index,1)*(E(alpha2_index,1)-E1)/k;
        if alpha2_new > V
            alpha2_new = V;
        elseif alpha2_new < U
            alpha2_new = U;
        end
        if abs(alpha2_new-alpha2) < littleValue
            continue
        else
            break
        end
    end
end