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"""
=========================================
SGD: Maximum margin separating hyperplane
=========================================
Plot the maximum margin separating hyperplane within a two-class
separable dataset using a linear Support Vector Machines classifier
trained using SGD.
"""
print __doc__
import numpy as np
import pylab as pl
from sklearn.linear_model import SGDClassifier
from sklearn.datasets.samples_generator import make_blobs
# we create 50 separable points
X, Y = make_blobs(n_samples=50, centers=2, random_state=0, cluster_std=0.60)
# fit the model
clf = SGDClassifier(loss="hinge", alpha=0.01, n_iter=200, fit_intercept=True)
clf.fit(X, Y)
# plot the line, the points, and the nearest vectors to the plane
xx = np.linspace(-1, 5, 10)
yy = np.linspace(-1, 5, 10)
X1, X2 = np.meshgrid(xx, yy)
Z = np.empty(X1.shape)
for (i, j), val in np.ndenumerate(X1):
x1 = val
x2 = X2[i, j]
p = clf.decision_function([x1, x2])
Z[i, j] = p[0]
levels = [-1.0, 0.0, 1.0]
linestyles = ['dashed', 'solid', 'dashed']
colors = 'k'
pl.contour(X1, X2, Z, levels, colors=colors, linestyles=linestyles)
pl.scatter(X[:, 0], X[:, 1], c=Y, cmap=pl.cm.Paired)
pl.axis('tight')
pl.show()
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