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# -*- coding: utf-8 -*-
"""
=========================================================
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.
"""
# Code source: Gaël Varoquaux
# Modified for documentation by Jaques Grobler
# License: BSD 3 clause
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
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
# 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",
cmap=cm.get_cmap("RdBu"),
)
plt.scatter(
X[:, 0], X[:, 1], c=Y, zorder=10, cmap=cm.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=cm.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()
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