SVM Diagram

Figure 9.9

Illustration of SVM. The region between the dashed lines is the margin, and the points which the dashed lines touch are called the support vectors.

Code output:

Python source code:

# Author: Jake VanderPlas
# License: BSD
#   The figure produced by this code is published in the textbook
#   "Statistics, Data Mining, and Machine Learning in Astronomy" (2013)
#   For more information, see http://astroML.github.com
#   To report a bug or issue, use the following forum:
#    https://groups.google.com/forum/#!forum/astroml-general
import numpy as np
from matplotlib import pyplot as plt
from sklearn import svm

#----------------------------------------------------------------------
# This function adjusts matplotlib settings for a uniform feel in the textbook.
# Note that with usetex=True, fonts are rendered with LaTeX.  This may
# result in an error if LaTeX is not installed on your system.  In that case,
# you can set usetex to False.
from astroML.plotting import setup_text_plots
setup_text_plots(fontsize=8, usetex=True)

#------------------------------------------------------------
# Create the data
np.random.seed(1)

N1 = 10
N2 = 10
mu1 = np.array([0, 0])
mu2 = np.array([2.0, 2.0])

Cov1 = np.array([[1, -0.5],
                [-0.5, 1]])
Cov2 = Cov1

X = np.vstack([np.random.multivariate_normal(mu1, Cov1, N1),
               np.random.multivariate_normal(mu2, Cov2, N2)])
y = np.hstack([np.zeros(N1), np.ones(N2)])

#------------------------------------------------------------
# Perform an SVM classification
clf = svm.SVC(kernel='linear')
clf.fit(X, y)

xx = np.linspace(-5, 5)
w = clf.coef_[0]
m = -w[0] / w[1]
b = - clf.intercept_[0] / w[1]
yy = m * xx + b

#------------------------------------------------------------
# find support vectors
i1 = np.argmax(np.dot(X[:N1], w))
i2 = N1 + np.argmin(np.dot(X[N1:], w))

db1 = X[i1, 1] - (m * X[i1, 0] + b)
db2 = X[i2, 1] - (m * X[i2, 0] + b)

#------------------------------------------------------------
# Plot the results
fig = plt.figure(figsize=(5, 3.75))
ax = fig.add_subplot(111, aspect='equal')

ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=plt.cm.binary)
ax.plot(xx, yy, '-k')
ax.plot(xx, yy + db1, '--k')
ax.plot(xx, yy + db2, '--k')

ax.set_ylim(-1.5, 4)
ax.set_xlim(-3, 4)

ax.set_xlabel('$x$')
ax.set_ylabel('$y$')

plt.show()

[download source: fig_svm_diagram.py]