matlab——SVM分類器

1.命令函數部分：

clear;%清屏
clc;
X =load('data.txt');
n = length(X);%總樣本數量
y = X(:,4);%類別標誌
X = X(:,1:3);
TOL = 0.0001;%精度要求
C = 1;%參數，對損失函數的權重
b = 0;%初始設置截距b
Wold = 0;%未更新a時的W(a)
Wnew = 0;%更新a後的W(a)
for i = 1 : 50%設置類別標誌爲1或者-1
    y(i) = -1;
end
a = zeros(n,1);%參數a
for i = 1 : n%隨機初始化a,a屬於[0,C]
        a(i) = 0.2;
end

%爲簡化計算，減少重複計算進行的計算
K = ones(n,n);
for i = 1 :n%求出K矩陣，便於之後的計算
    for j = 1 : n
        K(i,j) = k(X(i,:),X(j,:));
    end
end
sum = zeros(n,1);%中間變量，便於之後的計算，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%迭代過程
    
%啓發式選點
n1 = 1;%初始化，n1,n2代表選擇的2個點
n2 = 2;
%n1按照第一個違反KKT條件的點選擇
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|的原則選取
E1 = 0;
E2 = 0;
maxDiff = 0;%假設的最大誤差
E1 = sum(n1) + b - y(n1);%n1的誤差
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

%以下進行更新
a1old = a(n1);
a2old = a(n2);
KK = K(n1,n1) + K(n2,n2) - 2*K(n1,n2);
a2new = a2old + y(n2) *(E1 - E2) / KK;%計算新的a2
%a2必須滿足約束條件
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);%計算新的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後的W(a)
tempSum = 0;%臨時變量
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：通過找到某一個支持向量來計算
support = 1;%支持向量座標初始化
while abs(a(support))< 1e-4 && support <= n
    support = support + 1;
end
b = 1 / y(support) - sum(support);
%判斷停止條件
if abs(Wnew/ Wold - 1 ) <= TOL
    break;
end
end
%輸出結果：包括原分類，辨別函數計算結果，svm分類結果
for i = 1 : n
    fprintf('第%d點:原標號 ',i);
    if i <= 50
        fprintf('-1');
    else
        fprintf(' 1');
    end
    fprintf('    判別函數值%f      分類結果',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('歸類錯誤\n');
        end
    end
end

2.名爲f的功能函數部分:

function y = k(x1,x2)
    y = exp(-0.5*norm(x1 - x2).^2);
end

3.數據：
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