启发式选择

%%
%   svm 简单算法设计 --启发式选择
%%
clc
clear
close all
% step=0.05;error=1.2;
% [data, label]=generate_sample(step,error);
category=load(‘category.mat‘);
label=category.label;
feature=load(‘feature.mat‘);
data=feature.data;
[num_data,d] = size(data); % 样本数量，维度，维度在下面好像没有用到
%% 定义向量机参数
alphas = ones(num_data,1)-0.999999;
b = 0;
error = zeros(num_data,2);
tol = 0.001;
C = 600000;
iter = 0;
max_iter = 30;
alpha_change = 0;
entireSet = 1;%作为一个标记看是选择全遍历还是部分遍历

%第一个变量先遍历间隔边界（0<alpha<C）上的支持向量点（此时松弛变量等于0），检验其是否满足KKT条件，若全部满足再遍历整个样本
%第一个变量选取违反KKT条件最严重的样本点所对应的变量，意思是首先更新最糟糕的点
%选择第二个变量要使得|E1-E2|最大，即使得乘子的变化最大，要用启发式标准
%第二个变量的选择好像是先看有没有违反KKT条件的点，若有则选择，若没有则按照|E1-E2|来选择

while (iter < max_iter) && ((alpha_change > 0) || entireSet)
    alpha_change = 0;
    % -----------全遍历样本-------------------------
    if entireSet 
        for i = 1:num_data
            Ei = calEk(data,alphas,label,b,i);%计算误差
            %此处的条件既是选取第一个变量的标准，首先考虑的是间隔边界（0<alpha<C）上的支持向量点中不满足KKT条件的点所对应的变量
            %该条件困扰了我两天，实际上原来的写法过于虚伪，让人看不透摸不清，实际上写清楚了让人一看就明了。
            if (label(i)*Ei<-0.001 && alphas(i)<C)||(label(i)*Ei>0.001 && alphas(i)>0)
            %if (0<alphas(i) && alphas(i)<C && label(i)*Ei~=0)%写成这个形式要让alphas的初值大于零否则进不来循环体。
                %选择下一个alphas
                [j,Ej] = select(i,data,num_data,alphas,label,b,C,Ei,entireSet);
                alpha_I_old = alphas(i);
                alpha_J_old = alphas(j);
                if label(i) ~= label(j)
                    L = max(0,alphas(j) - alphas(i));
                    H = min(C,C + alphas(j) - alphas(i));
                else
                    L = max(0,alphas(j) + alphas(i) -C);
                    H = min(C,alphas(j) + alphas(i));
                end
                if L==H
                    continue;end
                eta = 2*data(i,:)*data(j,:)‘- data(i,:)*...
                    data(i,:)‘ - data(j,:)*data(j,:)‘;
                if eta >= 0 
                    continue;end
                alphas(j) = alphas(j) - label(j)*(Ei-Ej)/eta;
                %限制范围
                if alphas(j) > H
                    alphas(j) = H;
                elseif alphas(j) < L
                    alphas(j) = L;
                end
                if abs(alphas(j) - alpha_J_old) < 1e-4
                    continue;end
                alphas(i) = alphas(i) + label(i)*label(j)*(alpha_J_old-alphas(j));
                b1 = b - Ei - label(i)*(alphas(i)-alpha_I_old)*data(i,:)*data(i,:)‘- label(j)*(alphas(j)-alpha_J_old)*data(i,:)*data(j,:)‘;
                b2 = b - Ej - label(i)*(alphas(i)-alpha_I_old)*data(i,:)*data(j,:)‘- label(j)*(alphas(j)-alpha_J_old)*data(j,:)*data(j,:)‘;
                if (alphas(i) > 0) && (alphas(i) < C)
                    b = b1;
                elseif (alphas(j) > 0) && (alphas(j) < C)
                    b = b2;
                else
                    b = (b1+b2)/2;
                end
                alpha_change = alpha_change + 1;
            end
        end
         iter = iter + 1;
   % --------------部分遍历(alphas=0~C)的样本--------------------------
    else
        index = find(alphas>0 & alphas < C);
        for ii = 1:length(index)
            i = index(ii);
            Ei = calEk(data,alphas,label,b,i);%计算误差
            if (label(i)*Ei<-0.001 && alphas(i)<C)||...
                    (label(i)*Ei>0.001 && alphas(i)>0)
                %选择下一个样本
                [j,Ej] = select(i,data,num_data,alphas,label,b,C,Ei,entireSet);
                alpha_I_old = alphas(i);
                alpha_J_old = alphas(j);
                if label(i) ~= label(j)
                    L = max(0,alphas(j) - alphas(i));
                    H = min(C,C + alphas(j) - alphas(i));
                else
                    L = max(0,alphas(j) + alphas(i) -C);
                    H = min(C,alphas(j) + alphas(i));
                end
                if L==H
                    continue;end
                eta = 2*data(i,:)*data(j,:)‘- data(i,:)*...
                    data(i,:)‘ - data(j,:)*data(j,:)‘;
                if eta >= 0
                    continue;end
                alphas(j) = alphas(j) - label(j)*(Ei-Ej)/eta;  
                %限制范围
                if alphas(j) > H
                    alphas(j) = H;
                elseif alphas(j) < L
                    alphas(j) = L;
                end
                if abs(alphas(j) - alpha_J_old) < 1e-4
                    continue;end
                alphas(i) = alphas(i) + label(i)*...
                    label(j)*(alpha_J_old-alphas(j));
                b1 = b - Ei - label(i)*(alphas(i)-alpha_I_old)*...
                    data(i,:)*data(i,:)‘- label(j)*...
                    (alphas(j)-alpha_J_old)*data(i,:)*data(j,:)‘;
                b2 = b - Ej - label(i)*(alphas(i)-alpha_I_old)*...
                    data(i,:)*data(j,:)‘- label(j)*...
                    (alphas(j)-alpha_J_old)*data(j,:)*data(j,:)‘;
                if (alphas(i) > 0) && (alphas(i) < C)
                    b = b1;
                elseif (alphas(j) > 0) && (alphas(j) < C)
                    b = b2;
                else
                    b = (b1+b2)/2;
                end
                alpha_change = alpha_change + 1;
            end
        end
        iter = iter + 1;
    end
    % --------------------------------
    if entireSet %第一次全遍历了，下一次就变成部分遍历
        entireSet = 0;
    elseif alpha_change == 0 
        %如果部分遍历所有都没有找到需要交换的alpha，再改为全遍历
        entireSet = 1;
    end
    disp([‘iter ================== ‘,num2str(iter)]);    
end

% 计算权值W
W = (alphas.*label)‘*data;
%记录支持向量位置
index_sup = find(alphas ~= 0);
%计算预测结果
predict = (alphas.*label)‘*(data*data‘) + b;
predict = sign(predict);
% 显示结果
figure;
index1 = find(predict==-1);
data1 = (data(index1,:))‘;
plot(data1(1,:),data1(2,:),‘+r‘);
hold on
index2 = find(predict==1);
data2 = (data(index2,:))‘;
plot(data2(1,:),data2(2,:),‘*‘);
hold on
dataw = (data(index_sup,:))‘;
plot(dataw(1,:),dataw(2,:),‘og‘,‘LineWidth‘,2);
% 画出分界面，以及b上下正负1的分界面
hold on
k = -W(1)/W(2);
x = -1.2:0.1:1.2;
y = k*x + b;
plot(x,y,x,y-1,‘r--‘,x,y+1,‘r--‘);
title([‘松弛变量范围C = ‘,num2str(C)]);

function Ek = calEk(data,alphas,label,b,k)
pre_Li = (alphas.*label)‘*(data*data(k,:)‘) + b;
Ek = pre_Li - label(k);

function [J,Ej] = select(i,data,num_data,alphas,label,b,C,Ei,choose)
maxDeltaE = 0;maxJ = -1;
if choose == 1 %全遍历---随机选择alphas
    j = randi(num_data ,1);
    if j == i
        temp = 1;
        while temp
            j = randi(num_data,1);
            if j ~= i
                temp = 0;
            end
        end
    end
    J = j;
    Ej = calEk(data,alphas,label,b,J);
else %部分遍历--启发式的选择alphas
    index = find(alphas>0 & alphas < C);
    for k = 1:length(index)
        if i == index(k)
            continue;
        end
        temp_e = calEk(data,alphas,label,b,k);
        deltaE = abs(Ei - temp_e); %选择与Ei误差最大的alphas
        if deltaE > maxDeltaE
            maxJ = k;
            maxDeltaE = deltaE;
            Ej = temp_e;
        end
    end
    J = maxJ;
end