支持向量机（SVM）线性可分解决实例--参考麦子学院机器学习基础5.1

#首先产生数据集
#训练数据集
#画图展示超平面
import numpy as np
import pylab as pl
from sklearn import svm

# we create 40 separable points
#正态分布产生，均值分别为-2 2，可以线性可分
np.random.seed(0)
X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]
Y = [0]*20 +[1]*20

#fit the model
clf = svm.SVC(kernel='linear')
clf.fit(X, Y)

# get the separating hyperplane
w = clf.coef_[0]#权值
a = -w[0]/w[1]#直线斜率
xx = np.linspace(-5, 5)
yy = a*xx - (clf.intercept_[0])/w[1]

# plot the parallels to the separating hyperplane that pass through the support vectors
b = clf.support_vectors_[0]#前面的点位于左下角
yy_down = a*xx + (b[1] - a*b[0])
b = clf.support_vectors_[-1]#后面的点位于右上角
yy_up = a*xx + (b[1] - a*b[0])

print("w: ", w)
print("a: ", a)

# print "xx: ", xx
# print "yy: ", yy
print("support_vectors_: ", clf.support_vectors_)
print("clf.coef_: ", clf.coef_)

# switching to the generic n-dimensional parameterization of the hyperplan to the 2D-specific equation
# of a line y=a.x +b: the generic w_0x + w_1y +w_3=0 can be rewritten y = -(w_0/w_1) x + (w_3/w_1)

# plot the line, the points, and the nearest vectors to the plane
pl.plot(xx, yy, 'k-')
pl.plot(xx, yy_down, 'k--')
pl.plot(xx, yy_up, 'k--')

pl.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],
s=80, edgecolors='red')
pl.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired)
pl.axis('tight')
pl.show()