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SVM Margins Example#

The plots below illustrate the effect the parameter C has on the separation line. A large value of C basically tells our model that we do not have that much faith in our data’s distribution, and will only consider points close to line of separation.

A small value of C includes more/all the observations, allowing the margins to be calculated using all the data in the area.

plot svm margin
plot svm margin

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearnimport 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
# figure number
fignum = 1
# fit the model
for name, penalty in (("unreg", 1), ("reg", 0.05)):
 clf = svm.SVC (kernel="linear", C=penalty)
 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 (margin away from hyperplane in direction
 # perpendicular to hyperplane). This is sqrt(1+a^2) away vertically in
 # 2-d.
 margin = 1 / np.sqrt (np.sum (clf.coef_**2))
 yy_down = yy - np.sqrt (1 + a**2) * margin
 yy_up = yy + np.sqrt (1 + a**2) * margin
 # plot the line, the points, and the nearest vectors to the plane
 plt.figure (fignum, figsize=(4, 3))
 plt.clf ()
 plt.plot (xx, yy, "k-")
 plt.plot (xx, yy_down, "k--")
 plt.plot (xx, yy_up, "k--")
 plt.scatter (
 clf.support_vectors_[:, 0],
 clf.support_vectors_[:, 1],
 s=80,
 facecolors="none",
 zorder=10,
 edgecolors="k",
 )
 plt.scatter (
 X[:, 0], X[:, 1], c=Y, zorder=10, cmap=plt.get_cmap ("RdBu"), edgecolors="k"
 )
 plt.axis ("tight")
 x_min = -4.8
 x_max = 4.2
 y_min = -6
 y_max = 6
 YY, XX = np.meshgrid (yy, xx)
 xy = np.vstack ([XX.ravel(), YY.ravel()]).T
 Z = clf.decision_function(xy).reshape(XX.shape)
 # Put the result into a contour plot
 plt.contourf (XX, YY, Z, cmap=plt.get_cmap ("RdBu"), alpha=0.5, linestyles=["-"])
 plt.xlim (x_min, x_max)
 plt.ylim (y_min, y_max)
 plt.xticks (())
 plt.yticks (())
 fignum = fignum + 1
plt.show ()