"线性SVM"
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm

data = np.array([
    [0.1, 0.7],
    [0.3, 0.6],
    [0.4, 0.1],
    [0.5, 0.4],
    [0.8, 0.04],
    [0.42, 0.6],
    [0.9, 0.4],
    [0.6, 0.5],
    [0.7, 0.2],
    [0.7, 0.67],
    [0.27, 0.8],
    [0.5, 0.72]
])

label = [1] * 6 + [0] * 6
x_min,x_max = data[:, 0].min() - 0.2,data[:, 0].max() + 0.2
y_min,y_max = data[:, 1].min() - 0.2,data[:, 1].max() + 0.2
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.002),
            np.arange(y_min, y_max, 0.002))
model_linear = svm.SVC(kernel='linear', C = 0.001)
model_linear.fit(data,label) #训练
Z = model_linear.predict(np.c_[xx.ravel(),yy.ravel()]) #预测
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap = plt.cm.ocean, alpha = 0.6 )
plt.scatter(data[:6, 0], data[:6, 1], marker='o', color='r', s=100, lw=3) 
plt.scatter(data[6:, 0], data[6:, 1], marker='x', color='k', s=100, lw=3)
plt.title('Linear SVM')
plt.show()

plt.figure(figsize=(16,15))

for i, degree in enumerate([1, 3, 5, 7, 9, 12]):
    #C:惩罚系数，gamma：高斯核的系数
    model_poly = svm.SVC(C=0.0001, kernel='poly', degree=degree)
    model_poly.fit(data, label)
    #ravel-flatten
    #c_ -vstack
    # 把后面两个压扁之后变成了x1和x2，然后进行判断，得到结果在压缩成一个矩形
    Z = model_poly.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    plt.subplot(3, 2, i + 1)
    plt.subplots_adjust(wspace=0.4, hspace=0.4)
    plt.contourf(xx, yy, Z, cmap=plt.cm.ocean, alpha=0.6)
 
    # 画出训练点
    plt.scatter(data[:6, 0], data[:6, 1], marker='o', color='r', s=100, lw=3)
    plt.scatter(data[6:, 0], data[6:, 1], marker='x', color='k', s=100, lw=3)
    plt.title('Poly SVM with $\degree=$' + str(degree))
plt.show()

测试不同SVM在Mnist数据集上的分类情况

# C:软间隔惩罚系数
C_linear = 100
model_linear = svm.SVC(C = C_linear, kernel='linear').fit(X_train,y_train) # 线性核
print(f"Linear Kernel 's score: {model_linear.score(X_test,y_test)}")
for degree in range(1,10,2):
    model_poly = svm.SVC(C=100, kernel='poly', degree=degree).fit(X_train,y_train) # 多项式核
    print(f"Polynomial Kernel with Degree = {degree} 's score: {model_poly.score(X_test,y_test)}")

for gamma in range(1,10,2):
    gamma = round(0.01 * gamma,3)
    model_rbf = svm.SVC(C = 100, kernel='rbf', gamma = gamma).fit(X_train,y_train) # 高斯核
    print(f"Polynomial Kernel with Gamma = {gamma} 's score: {model_rbf.score(X_test,y_test)}")

# Mnsit有0-9十个标记，由于是二分类任务，所以可以将标记0的作为1，其余为0用于识别是否为0的任务
y_train=np.array([1 if y_train[i]==1 else 0 for i in range(len(y_train))])
y_test=np.array([1 if y_test[i]==1 else 0 for i in range(len(y_test))])
# C:软间隔惩罚系数
C_linear = 100

model_linear = svm.SVC(C = C_linear, kernel='linear').fit(X_train,y_train) # 线性核
print(f"Linear Kernel 's score: {model_linear.score(X_test,y_test)}")

for degree in range(1,10,2):
    model_poly = svm.SVC(C=100, kernel='poly', degree=degree).fit(X_train,y_train) # 多项式核
    print(f"Polynomial Kernel with Degree = {degree} 's score: {model_poly.score(X_test,y_test)}")

for gamma in range(1,10,2):
    gamma = round(0.01 * gamma,3)
    model_rbf = svm.SVC(C = 100, kernel='rbf', gamma = gamma).fit(X_train,y_train) # 高斯核
    print(f"Polynomial Kernel with Gamma = {gamma} 's score: {model_rbf.score(X_test,y_test)}")

https://github.com/datawhalechina/machine-learning-toy-code/blob/main/ml-with-sklearn/SVM/SVM.ipynb