SVM算法Python实现

  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