Python机器学习应用之支持向量机的分类预测篇

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
X, y = make_blobs(n_samples=60, centers=2, random_state=0, cluster_std=0.4)
x_fit = np.linspace(0, 3)
#使用SVM
from sklearn.svm import SVC
# SVM 函数
clf = SVC(kernel='linear')
clf.fit(X, y)
# 最佳函数
w = clf.coef_[0]
a = -w[0] / w[1]
y_p = a*x_fit - (clf.intercept_[0]) / w[1]

# 最大边距 下边界
b_down = clf.support_vectors_[0]
y_down = a* x_fit + b_down[1] - a * b_down[0]
# 最大边距 上届
b_up = clf.support_vectors_[-1]
y_up = a* x_fit + b_up[1] - a * b_up[0]

# 画散点图
X, y = make_blobs(n_samples=60, centers=2, random_state=0, cluster_std=0.4)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.Paired)
# 画函数
plt.plot(x_fit, y_p, '-c')
# 画边距
plt.fill_between(x_fit, y_down, y_up, edgecolor='none', color='#AAAAAA', alpha=0.4)
# 画支持向量
plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], edgecolor='b',
            s=80, facecolors='none')

#%%软间隔
X, y = make_blobs(n_samples=60, centers=2, random_state=0, cluster_std=0.9)
x_fit = np.linspace(-2, 4)
# 惩罚参数：C=1，
clf = SVC(C=1, kernel='linear')
clf.fit(X, y)

# 最佳函数
w = clf.coef_[0]
a = -w[0] / w[1]
y_great = a*x_fit - (clf.intercept_[0]) / w[1]
# 最大边距 下边界
b_down = clf.support_vectors_[0]
y_down = a* x_fit + b_down[1] - a * b_down[0]
# 最大边距 上边界
b_up = clf.support_vectors_[-1]
y_up = a* x_fit + b_up[1] - a * b_up[0]
# 画散点图
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.Paired)
# 画函数
plt.plot(x_fit, y_great, '-c')
# 画边距
plt.fill_between(x_fit, y_down, y_up, edgecolor='none', color='#AAAAAA', alpha=0.4)
# 画支持向量
plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], edgecolor='b',
            s=80, facecolors='none')

#%%超平面
from sklearn.datasets import make_circles
# 画散点图
X, y = make_circles(100, factor=.1, noise=.1, random_state=2019)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.Paired)

# 数据映射
r = np.exp(-(X[:, 0] ** 2 + X[:, 1] ** 2))

ax = plt.subplot(projection='3d')
ax.scatter3D(X[:, 0], X[:, 1], r, c=y, s=50, cmap=plt.cm.Paired)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')

x_1, y_1 = np.meshgrid(np.linspace(-1, 1), np.linspace(-1, 1))
z =  0.01*x_1 + 0.01*y_1 + 0.5
ax.plot_surface(x_1, y_1, z, alpha=0.3)

#%%使用高斯核函数实现这种分类：kernel=‘rbf'
# 画图
X, y = make_circles(100, factor=.1, noise=.1, random_state=2019)
plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.Paired)
clf = SVC(kernel='rbf')
clf.fit(X, y)

ax = plt.gca()
x = np.linspace(-1, 1)
y = np.linspace(-1, 1)
x_1, y_1 = np.meshgrid(x, y)
P = np.zeros_like(x_1)
for i, xi in enumerate(x):
    for j, yj in enumerate(y):
        P[i, j] = clf.decision_function(np.array([[xi, yj]]))
ax.contour(x_1, y_1, P, colors='k', levels=[-1, 0, 0.9], alpha=0.5,linestyles=['--', '-', '--'])
plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], edgecolor='b',s=80, facecolors='none');