1. 导入数据

from sklearn import datasets

iris = datasets.load_iris()

X = iris.data
y = iris.target

X = X[y<2,:2]
y = y[y<2]

plt.scatter(X[y==0,0], X[y==0,1], color='red')
plt.scatter(X[y==1,0], X[y==1,1], color='blue')
plt.show()
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
​
iris = datasets.load_iris()
​
X = iris.data
y = iris.target
​
X = X[y<2,:2]
y = y[y<2]
​
plt.scatter(X[y==0,0], X[y==0,1], color='red')
plt.scatter(X[y==1,0], X[y==1,1], color='blue')
plt.show()

2. 数据归一化

from sklearn.preprocessing import StandardScaler

standardScaler = StandardScaler()
standardScaler.fit(X)
X_standard = standardScaler.transform(X)

3. Hard Margin SVM

from sklearn.svm import LinearSVC
# 当C无限大时，ζ约为 0，此时就是Hard Margin SVM
svc = LinearSVC(C=1e9)
svc.fit(X_standard,y)C

绘制图像

def plot_svc_decision_boundary(model, axis):
    
    x0, x1 = np.meshgrid(
        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),
        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),
    )
    X_new = np.c_[x0.ravel(), x1.ravel()]

    y_predict = model.predict(X_new)
    zz = y_predict.reshape(x0.shape)

    from matplotlib.colors import ListedColormap
    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])
    
    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)
    
    w = model.coef_[0]
    b = model.intercept_[0]
    
    # w0*x0 + w1*x1 + b = 0
    # => x1 = -w0/w1 * x0 - b/w1
    plot_x = np.linspace(axis[0], axis[1], 200)
    up_y = -w[0]/w[1] * plot_x - b/w[1] + 1/w[1]
    down_y = -w[0]/w[1] * plot_x - b/w[1] - 1/w[1]
    
    up_index = (up_y >= axis[2]) & (up_y <= axis[3])
    down_index = (down_y >= axis[2]) & (down_y <= axis[3])
    plt.plot(plot_x[up_index], up_y[up_index], color='black')
    plt.plot(plot_x[down_index], down_y[down_index], color='black')

plot_svc_decision_boundary(svc, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[y==0,0], X_standard[y==0,1])
plt.scatter(X_standard[y==1,0], X_standard[y==1,1])
plt.show()

4. Soft Margin SVM

svc2 = LinearSVC(C=0.01)
svc2.fit(X_standard, y)

绘制图像

plot_svc_decision_boundary(svc2, axis=[-3, 3, -3, 3])
plt.scatter(X_standard[y==0,0], X_standard[y==0,1])
plt.scatter(X_standard[y==1,0], X_standard[y==1,1])
plt.show()