机器学习算法原理实现——跟着gpt学习svm求解的SMO算法
算法实现:
import numpy as np from sklearn.metrics import confusion_matrix import matplotlib.pyplot as plt import random as rnd class SVM(): def __init__(self, max_iter=100, kernel_type='linear', C=1.0, epsilon=0.001): self.kernels = { 'linear' : self.kernel_linear, 'quadratic' : self.kernel_quadratic, 'gaussian' : self.kernel_gauss } self.max_iter = max_iter self.kernel_type = kernel_type self.C = C self.epsilon = epsilon def fit(self, X, y): n, d = X.shape[0], X.shape[1] alpha = np.zeros((n)) kernel = self.kernels[self.kernel_type] count = 0 while True: count += 1 alpha_prev = np.copy(alpha) for j in range(0, n): i = self.get_rnd_int(0, n-1, j) # Get random int i~=j x_i, x_j, y_i, y_j = X[i,:], X[j,:], y[i], y[j] k_ij = kernel(x_i, x_i) + kernel(x_j, x_j) - 2 * kernel(x_i, x_j) if k_ij == 0: continue alpha_prime_j, alpha_prime_i = alpha[j], alpha[i] (L, H) = self.compute_L_H(self.C, alpha_prime_j, alpha_prime_i, y_j, y_i) # Compute model parameters self.w = self.calc_w(alpha, y, X) self.b = self.calc_b(X, y, self.w) # Compute E_i, E_j E_i = self.E(x_i, y_i, self.w, self.b) E_j = self.E(x_j, y_j, self.w, self.b) # Set new alpha values alpha[j] = alpha_prime_j + float(y_j * (E_i - E_j))/k_ij alpha[j] = max(alpha[j], L) alpha[j] = min(alpha[j], H) alpha[i] = alpha_prime_i + y_i*y_j * (alpha_prime_j - alpha[j]) # if(j % 100 == 0): # print(j) # Check convergence diff = np.linalg.norm(alpha - alpha_prev) if diff < self.epsilon: break #print(count) if count >= self.max_iter: print("Iteration number exceeded the max of %d iterations" % (self.max_iter)) return self.b = self.calc_b(X, y, self.w) if self.kernel_type == 'linear': self.w = self.calc_w(alpha, y, X) # Get support vectors alpha_idx = np.where(alpha > 0)[0] support_vectors = X[alpha_idx, :] return support_vectors, count def predict(self, X): return self.h(X, self.w, self.b) def calc_b(self, X, y, w): b_tmp = y - np.dot(w.T, X.T) return np.mean(b_tmp) def calc_w(self, alpha, y, X): return np.dot(X.T, np.multiply(alpha,y)) def h(self, X, w, b): return np.sign(np.dot(w.T, X.T) + b).astype(int) def E(self, x_k, y_k, w, b): return self.h(x_k, w, b) - y_k def compute_L_H(self, C, alpha_prime_j, alpha_prime_i, y_j, y_i): if(y_i != y_j): return (max(0, alpha_prime_j - alpha_prime_i), min(C, C - alpha_prime_i + alpha_prime_j)) else: return (max(0, alpha_prime_i + alpha_prime_j - C), min(C, alpha_prime_i + alpha_prime_j)) def get_rnd_int(self, a,b,z): i = z cnt=0 while i == z and cnt<1000: i = rnd.randint(a,b) cnt=cnt+1 return i def kernel_linear(self, x1, x2): return np.dot(x1, x2.T) def kernel_quadratic(self, x1, x2): return (np.dot(x1, x2.T) ** 2) def kernel_gauss(self,x1, x2, sigma=1): return np.exp(- (np.linalg.norm(x1 - x2, 2)) ** 2 / (2 * sigma ** 2)) def predict_proba(self, X): return np.dot(self.w.T, X.T) + self.b import matplotlib.pyplot as plt # 给定二维正态分布均值矩阵 mean1, mean2 = np.array([0, 2]), np.array([2, 0]) # 给定二维正态分布协方差矩阵 covar = np.array([[1.5, 1.0], [1.0, 1.5]]) # 生成二维正态分布样本X1 X1 = np.random.multivariate_normal(mean1, covar, 100) # 生成X1的标签1 y1 = np.ones(X1.shape[0]) # 生成二维正态分布样本X2 X2 = np.random.multivariate_normal(mean2, covar, 100) # 生成X1的标签-1 y2 = -1 * np.ones(X2.shape[0]) # 设置训练集和测试集 X_train = np.vstack((X1[:80], X2[:80])) y_train = np.hstack((y1[:80], y2[:80])) X_test = np.vstack((X1[80:], X2[80:])) y_test = np.hstack((y1[80:], y2[80:])) X, y = X_train, y_train model = SVM(max_iter=3, kernel_type='linear', C=3.0, epsilon=0.001) model.fit(X_train, y_train) y_predicted = [model.predict(x) for x in X_test] cm = confusion_matrix(y_test, y_predicted) accuracy = (cm[0][0] + cm[1][1]) / (cm[0][0] + cm[0][1] + cm[1][0] + cm[1][1]) print(accuracy) # 画图展示 fig, ax = plt.subplots() colors = ['red' if c == -1 else 'blue' for c in y] ax.scatter(X[:, 0], X[:, 1], c=colors) # 创建决策边界 xx = np.linspace(-3, 7, 10) yy = - (model.w[0] * xx + model.b) / model.w[1] ax.plot(xx, yy, color='green', linestyle='-') plt.show()
运行结果:
Iteration number exceeded the max of 3 iterations
0.975 精度还不错!
使用sklearn的库:
# 导入svm模块 from sklearn import svm # 创建svm模型实例 clf = svm.SVC(kernel='linear') # 模型拟合 clf.fit(X_train, y_train) # 模型预测 y_pred = clf.predict(X_test) # 计算测试集上的分类准确率 cm = confusion_matrix(y_test, y_predicted) accuracy = (cm[0][0] + cm[1][1]) / (cm[0][0] + cm[0][1] + cm[1][0] + cm[1][1]) print(accuracy)
精度也是一样!