1 class SVM: 2 def __init__(self, max_iter=100, kernel='linear'): 3 self.max_iter = max_iter 4 self._kernel = kernel 5 6 def init_args(self, features, labels): 7 self.m, self.n = features.shape 8 self.X = features 9 self.Y = labels 10 self.b = 0.0 11 12 # 将Ei保存在一个列表里 13 self.alpha = np.ones(self.m) 14 self.E = [self._E(i) for i in range(self.m)] 15 # 松弛变量 16 self.C = 1.0 17 18 def _KKT(self, i): 19 y_g = self._g(i) * self.Y[i] 20 if self.alpha[i] == 0: 21 return y_g >= 1 22 elif 0 < self.alpha[i] < self.C: 23 return y_g == 1 24 else: 25 return y_g <= 1 26 27 # g(x)预测值，输入xi（X[i]） 28 def _g(self, i): 29 r = self.b 30 for j in range(self.m): 31 r += self.alpha[j] * self.Y[j] * self.kernel(self.X[i], self.X[j]) 32 return r 33 34 # 核函数 35 def kernel(self, x1, x2): 36 if self._kernel == 'linear': 37 return sum([x1[k] * x2[k] for k in range(self.n)]) 38 elif self._kernel == 'poly': 39 return (sum([x1[k] * x2[k] for k in range(self.n)]) + 1)**2 40 41 return 0 42 43 # E（x）为g(x)对输入x的预测值和y的差 44 def _E(self, i): 45 return self._g(i) - self.Y[i] 46 47 def _init_alpha(self): 48 # 外层循环首先遍历所有满足0<a<C的样本点，检验是否满足KKT 49 index_list = [i for i in range(self.m) if 0 < self.alpha[i] < self.C] 50 # 否则遍历整个训练集 51 non_satisfy_list = [i for i in range(self.m) if i not in index_list] 52 index_list.extend(non_satisfy_list) 53 54 for i in index_list: 55 if self._KKT(i): 56 continue 57 58 E1 = self.E[i] 59 # 如果E1是+，选择最小的；如果E1是负的，选择最大的 60 if E1 >= 0: 61 j = min(range(self.m), key=lambda x: self.E[x]) 62 else: 63 j = max(range(self.m), key=lambda x: self.E[x]) 64 return i, j 65 66 def _compare(self, _alpha, L, H): 67 if _alpha > H: 68 return H 69 elif _alpha < L: 70 return L 71 else: 72 return _alpha 73 74 def fit(self, features, labels): 75 self.init_args(features, labels) 76 77 for t in range(self.max_iter): 78 # train 79 i1, i2 = self._init_alpha() 80 81 # 设定边界 82 if self.Y[i1] == self.Y[i2]: 83 L = max(0, self.alpha[i1] + self.alpha[i2] - self.C) 84 H = min(self.C, self.alpha[i1] + self.alpha[i2]) 85 else: 86 L = max(0, self.alpha[i2] - self.alpha[i1]) 87 H = min(self.C, self.C + self.alpha[i2] - self.alpha[i1]) 88 89 E1 = self.E[i1] 90 E2 = self.E[i2] 91 # eta=K11+K22-2K12 92 eta = self.kernel(self.X[i1], self.X[i1]) + self.kernel( 93 self.X[i2], 94 self.X[i2]) - 2 * self.kernel(self.X[i1], self.X[i2]) 95 if eta <= 0: 96 # print('eta <= 0') 97 continue 98 99 alpha2_new_unc = self.alpha[i2] + self.Y[i2] * ( 100 E1 - E2) / eta # 第二版统计学习方法 P142~148
101 alpha2_new = self._compare(alpha2_new_unc, L, H) # 若超过边界，将alpha设定为边界值 102 103 alpha1_new = self.alpha[i1] + self.Y[i1] * self.Y[i2] * ( 104 self.alpha[i2] - alpha2_new) 105 106 b1_new = -E1 - self.Y[i1] * self.kernel(self.X[i1], self.X[i1]) * ( 107 alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel( 108 self.X[i2], 109 self.X[i1]) * (alpha2_new - self.alpha[i2]) + self.b 110 b2_new = -E2 - self.Y[i1] * self.kernel(self.X[i1], self.X[i2]) * ( 111 alpha1_new - self.alpha[i1]) - self.Y[i2] * self.kernel( 112 self.X[i2], 113 self.X[i2]) * (alpha2_new - self.alpha[i2]) + self.b 114 115 if 0 < alpha1_new < self.C: 116 b_new = b1_new 117 elif 0 < alpha2_new < self.C: 118 b_new = b2_new 119 else: 120 # 选择中点 121 b_new = (b1_new + b2_new) / 2 122 123 # 更新参数 124 self.alpha[i1] = alpha1_new 125 self.alpha[i2] = alpha2_new 126 self.b = b_new 127 128 self.E[i1] = self._E(i1) 129 self.E[i2] = self._E(i2) 130 return 'train done!' 131 132 def predict(self, data): 133 r = self.b 134 for i in range(self.m): 135 r += self.alpha[i] * self.Y[i] * self.kernel(data, self.X[i]) 136 137 return 1 if r > 0 else -1 138 139 def score(self, X_test, y_test): 140 right_count = 0 141 for i in range(len(X_test)): 142 result = self.predict(X_test[i]) 143 if result == y_test[i]: 144 right_count += 1 145 return right_count / len(X_test) 146 147 def _weight(self): 148 # linear model 149 yx = self.Y.reshape(-1, 1) * self.X 150 self.w = np.dot(yx.T, self.alpha) 151 return self.w
参照周志华西瓜书关于SVM的推导，有助于理解
程序可以结合机器学习实战关于SVM代码部分学习