1.命令函数部分：
clear;%清屏
clc;
X =load('data.txt');
n = length(X);%总样本数量
y = X(:,4);%类别标志
X = X(:,1:3);
TOL = 0.0001;%精度要求
C = 1;%参数，对损失函数的权重
b = 0;%初始设置截距b
Wold = 0;%未更新a时的W(a)
Wnew = 0;%更新a后的W(a)
for i = 1 : 50%设置类别标志为1或者-1
y(i) = -1;
end
a = zeros(n,1);%参数a
for i = 1 : n%随机初始化a,a属于[0,C]
a(i) = 0.2;
end
%为简化计算，减少重复计算进行的计算
K = ones(n,n);
for i = 1 :n%求出K矩阵，便于之后的计算
for j = 1 : n
K(i,j) = k(X(i,:),X(j,:));
end
end
sum = zeros(n,1);%中间变量，便于之后的计算，sum(k)=sigma a(i)*y(i)*K(k,i);
for k = 1 : n
for i = 1 : n
sum(k) = sum(k) + a(i) * y(i) * K(i,k);
end
end
while 1%迭代过程
%启发式选点
n1 = 1;%初始化，n1,n2代表选择的2个点
n2 = 2;
%n1按照第一个违反KKT条件的点选择
while n1 <= n
if y(n1) * (sum(n1) + b) == 1 && a(n1) >= C && a(n1) <= 0
break;
end
if y(n1) * (sum(n1) + b) > 1 && a(n1) ~= 0
break;
end
if y(n1) * (sum(n1) + b) < 1 && a(n1) ~=C
break;
end
n1 = n1 + 1;
end
%n2按照最大化|E1-E2|的原则选取
E1 = 0;
E2 = 0;
maxDiff = 0;%假设的最大误差
E1 = sum(n1) + b - y(n1);%n1的误差
for i = 1 : n
tempSum = sum(i) + b - y(i);
if abs(E1 - tempSum)> maxDiff
maxDiff = abs(E1 - tempSum);
n2 = i;
E2 = tempSum;
end
end
%以下进行更新
a1old = a(n1);
a2old = a(n2);
KK = K(n1,n1) + K(n2,n2) - 2*K(n1,n2);
a2new = a2old + y(n2) *(E1 - E2) / KK;%计算新的a2
%a2必须满足约束条件
S = y(n1) * y(n2);
if S == -1
U = max(0,a2old - a1old);
V = min(C,C - a1old + a2old);
else
U = max(0,a1old + a2old - C);
V = min(C,a1old + a2old);
end
if a2new > V
a2new = V;
end
if a2new < U
a2new = U;
end
a1new = a1old + S * (a2old - a2new);%计算新的a1
a(n1) = a1new;%更新a
a(n2) = a2new;
%更新部分值
sum = zeros(n,1);
for k = 1 : n
for i = 1 : n
sum(k) = sum(k) + a(i) * y(i) * K(i,k);
end
end
Wold = Wnew;
Wnew = 0;%更新a后的W(a)
tempSum = 0;%临时变量
for i = 1 : n
for j = 1 : n
tempSum= tempSum + y(i )*y(j)*a(i)*a(j)*K(i,j);
end
Wnew= Wnew+ a(i);
end
Wnew= Wnew - 0.5 * tempSum;
%以下更新b：通过找到某一个支持向量来计算
support = 1;%支持向量坐标初始化
while abs(a(support))< 1e-4 && support <= n
support = support + 1;
end
b = 1 / y(support) - sum(support);
%判断停止条件
if abs(Wnew/ Wold - 1 ) <= TOL
break;
end
end
%输出结果：包括原分类，辨别函数计算结果，svm分类结果
for i = 1 : n
fprintf('第%d点:原标号 ',i);
if i <= 50
fprintf('-1');
else
fprintf(' 1');
end
fprintf(' 判别函数值%f 分类结果',sum(i) + b);
if abs(sum(i) + b - 1) < 0.5
fprintf('1\n');
else if abs(sum(i) + b + 1) < 0.5
fprintf('-1\n');
else
fprintf('归类错误\n');
end
end
end
2.名为f的功能函数部分:
function y = k(x1,x2)
y = exp(-0.5*norm(x1 - x2).^2);
end
3.数据：
0.8871 -0.3491 8.3376 0
1.2519 1.2083 6.5041 0
-1.1925 1.9338 1.8790 0
-0.1277 2.4371 2.6971 0
1.9697 3.0906 6.0391 0
0.7603 0.8241 1.5323 0
1.6382 3.5516 4.4694 0
1.3438 -0.4539 5.9366 0
-1.3361 -2.0201 1.6393 0
-0.3886 3.3041 8.0450 0
-0.6780 6.0196 -0.4084 0
0.3552 -0.1051 1.2458 0
1.6560 4.0786 0.8521 0
0.8117 3.5451 6.8925 0
1.4773 -1.9340 3.9256 0
-0.0732 -0.9526 0.4609 0
0.1521 4.3711 2.2600 0
1.4820 0.7493 0.3475 0
0.6140 4.5261 8.3776 0
0.5721 3.3460 3.7853 0
0.5269 4.1452 4.3900 0
1.7879 -0.5390 2.5516 0
0.9885 5.7625 0.1832 0
-0.3318 2.4373 -0.6884 0
1.3578 5.4709 3.4302 0
2.7210 -1.1268 4.7719 0
0.5039 -0.1025 2.3650 0
1.1107 1.6885 3.7650 0
0.7862 1.3587 7.3203 0
1.0444 -1.5841 3.6349 0
1.7795 1.7276 4.9847 0
0.6710 1.4724 -0.5504 0
0.2303 0.2720 -1.6028 0
1.7089 -1.7399 4.8882 0
1.0059 0.5557 5.1188 0
2.3050 0.8545 2.8294 0
1.9555 0.9898 0.3501 0
1.7141 1.5413 3.8739 0
2.2749 5.3280 4.9604 0
1.6171 0.5270 3.3826 0
3.6681 -1.8409 4.8934 0
1.1964 1.8781 1.4146 0
0.7788 2.1048 0.0380 0
0.7916 5.0906 3.8513 0
1.0807 1.8849 5.9766 0
0.6340 2.6030 3.6940 0
1.9069 -0.0609 7.4208 0
1.6599 4.9409 8.1108 0
1.3763 0.8899 3.9069 0
0.8485 1.4688 6.7393 0
3.6792 6.1092 4.9051 1
4.3812 7.2148 6.1211 1
4.3971 3.4139 7.7974 1
5.0716 7.7253 10.5373 1
5.3078 8.8138 6.1682 1
4.1448 5.5156 2.8731 1
5.3609 6.0458 4.0815 1
4.7452 6.6352 1.3689 1
6.0274 6.5397 -1.9120 1
5.3174 3.0134 6.7935 1
7.2459 3.6970 3.1246 1
6.1007 8.1087 5.5568 1
5.9924 6.9238 5.7938 1
6.0263 5.3333 7.5185 1
3.6470 8.0915 6.4713 1
3.6543 7.2264 7.5783 1
5.0114 6.5335 3.5229 1
4.4348 7.4379 -0.0292 1
3.6087 3.7351 3.0172 1
3.5374 5.5354 7.6578 1
6.0048 2.0691 10.4513 1
3.1423 4.0003 5.4994 1
3.4012 7.1536 8.3510 1
5.5471 5.1372 -1.5090 1
6.5089 5.4911 8.0468 1
5.4583 6.7674 5.9353 1
4.1727 2.9798 3.6027 1
5.1672 8.4136 4.8621 1
4.8808 3.5514 1.9953 1
5.4938 4.1998 3.2440 1
5.4542 5.8803 4.4269 1
4.8743 3.9641 8.1417 1
5.9762 6.7711 2.3816 1
6.6945 7.2858 1.8942 1
4.7301 5.7652 1.6608 1
4.7084 5.3623 3.2596 1
6.0408 3.3138 7.7876 1
4.6024 8.3517 0.2193 1
4.7054 6.6633 -0.3492 1
4.7139 5.6362 6.2330 1
4.0850 10.7118 3.3541 1
6.1088 6.1635 4.2292 1
4.9836 5.4042 6.7422 1
6.1387 6.1949 2.5614 1
6.0700 7.0373 3.3256 1
5.6881 5.1363 9.9254 1
7.2058 2.3570 4.7361 1
4.2972 7.3245 4.7928 1
4.7794 8.1235 3.1827 1
3.9282 6.4092 -0.6339 1
