机器学习-支持向量机理论与应用（一）

# -*- coding:utf-8 -*-

from sklearn import svm

x = [[2,0],[1,1],[2,3]]
#python中的两类问题分类标签
y = [0,0,1]

clf = svm.SVC(kernel=‘linear‘)
clf.fit(x,y)

print(clf)

#get support vectors 支持向量
print(clf.support_vectors_)

#get index of support vectors 支持向量的下标
print(clf.support_)

#get number of support vectors for each class
print(clf.n_support_)

SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
  decision_function_shape=None, degree=3, gamma=‘auto‘, kernel=‘linear‘,
  max_iter=-1, probability=False, random_state=None, shrinking=True,
  tol=0.001, verbose=False)
[[ 1.  1.]
 [ 2.  3.]]
[1 2]
[1 1]

# -*- coding:utf-8 -*-

import numpy as np
import pylab as pl
from sklearn import  svm

#we create 40 separable points
np.random.seed(0)#控制每次的数据相同
#- [2,2] + [2,2] 是为了使得两组正态分布的数据呈线性上下分开
X = np.r_[np.random.randn(20,2) - [2,2], np.random.randn(20,2) + [2,2]]
Y = [0]*20 + [1]*20 #类标签

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

#get the separating hyperplane
w = clf.coef_[0]
a = -w[0] / w[1] #斜率
xx = np.linspace(-5,5) #[-5,-4,-3,...,5]
#clf.intercept_[0]) 为w[3]
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]#取出第一个支持向量
yy_down = a * xx + (b[1] - a*b[0]) #(b[1] - a*b[0])下面直线的截距
b = clf.support_vectors_[-1]#最后一个支持向量
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, facecolors=‘none‘)
pl.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired)

pl.axis(‘tight‘)
pl.show()

w:  [ 0.90230696  0.64821811]
a:  -1.39198047626
support_vectors_:  [[-1.02126202  0.2408932 ]
 [-0.46722079 -0.53064123]
 [ 0.95144703  0.57998206]]
clf.coef_:  [[ 0.90230696  0.64821811]]