import numpy as np import matplotlib.pyplot as plt from sklearn.svm import SVC from sklearn.datasets.samples_generator import make_circles X, y = make_circles(100, factor=.1, noise=.1) plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')对上述数据集，用高斯核函数非线性支持向量机进行分类，并绘制出决策边界和支持向量

代码如下：

# 构造高斯核函数
def gaussian_kernel(x1, x2):
    sigma = 0.1
    return np.exp(-np.sum((x1 - x2) ** 2) / (2 * sigma ** 2))

# 定义模型并训练
svm = SVC(kernel=gaussian_kernel)
svm.fit(X, y)

# 绘制决策边界和支持向量
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='autumn')
plt.xlim(-1.5, 1.5)
plt.ylim(-1.5, 1.5)

ax = plt.gca()
x_vals = np.linspace(-1.5, 1.5, 50)
y_vals = np.linspace(-1.5, 1.5, 50)
z_vals = np.zeros((50, 50))
for i, xi in enumerate(x_vals):
    for j, yj in enumerate(y_vals):
        z_vals[i, j] = svm.predict(np.array([[xi, yj]]))

ax.contour(x_vals, y_vals, z_vals, levels=[-0.5, 0.5], linestyles=['--', '-'])
plt.scatter(svm.support_vectors_[:, 0], svm.support_vectors_[:, 1], s=100, linewidth=1, facecolors='none')
plt.show()

结果如下图所示：