Support Vector Machine(2)

1 sklearn简单例子

from sklearn import svm

X = [[2, 0], [1, 1], [2,3]]

y = [0, 0, 1]

clf = svm.SVC(kernel = 'linear')

clf.fit(X, y)  

print clf

# get support vectors

print clf.support_vectors_

# get indices of support vectors

print clf.support_ 

# get number of support vectors for each class

print clf.n_support_ 

2 sklearn画出决定界限

print(__doc__)

import numpy as np

import pylab as pl

from sklearn import svm

# we create 40 separable points

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 coef是线性回归，指的是系数

w = clf.coef_[0]

a = -w[0] / w[1]

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]

yy_down = a * xx + (b[1] - a * b[0])

b = clf.support_vectors_[-1]

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_

# In scikit-learn coef_ attribute holds the vectors of the separating hyperplanes for linear models. It has shape (n_classes, n_features) if n_classes > 1 (multi-class one-vs-all) and (1, n_features) for binary classification.

# 

# In this toy binary classification example, n_features == 2, hence w = coef_[0] is the vector orthogonal to the hyperplane (the hyperplane is fully defined by it + the intercept).

# 

# To plot this hyperplane in the 2D case (any hyperplane of a 2D plane is a 1D line), we want to find a f as in y = f(x) = a.x + b. In this case a is the slope of the line and can be computed by a = -w[0] / w[1].

# plot the line, the points, and the nearest vectors to the plane

pl.plot(xx, yy, 'k-')  //黑色实线

pl.plot(xx, yy_down, 'k--')//黑色短线

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()