"""
===========================================
SVM: Maximum margin separating hyperplane
===========================================

Plot the maximum margin separating hyperplane within a two-class
separable dataset using a Support Vector Machines classifier with
linear kernel.
"""

import numpy as np
import pylab as pl
from scikits.learn 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
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])

# plot the line, the points, and the nearest vectors to the plane
pl.set_cmap(pl.cm.Paired)
pl.plot(xx, yy, 'k-')
pl.plot(xx, yy_down, 'k--')
pl.plot(xx, yy_up, 'k--')
pl.scatter(X[:,0], X[:,1], c=Y)
pl.scatter(clf.support_vectors_[:,0], clf.support_vectors_[:,1], c='white')

pl.axis('tight')
pl.show()