Penalty¶
The below penalty cases, are predicated on the following:
# classifying packages
import numpy as np
from sklearn.svm import SVC
# visualizer packages
from matplotlib.colors import ListedColormap
import matplotlib.pyplot as plt
import warnings
def versiontuple(v):
return tuple(map(int, (v.split('.'))))
def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02):
# setup marker generator and color map
markers = ('s', 'x', 'o', '^', 'v')
colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
# plot the decision surface
x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx1, xx2 = np.meshgrid(
np.arange(
x1_min,
x1_max,
resolution
),
np.arange(x2_min, x2_max, resolution)
)
Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
Z = Z.reshape(xx1.shape)
plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
plt.xlim(xx1.min(), xx1.max())
plt.ylim(xx2.min(), xx2.max())
for idx, cl in enumerate(np.unique(y)):
plt.scatter(
x=X[y == cl, 0],
y=X[y == cl, 1],
alpha=0.8,
c=cmap(idx),
marker=markers[idx],
label=cl
)
# highlight test samples
if test_idx:
# plot all samples
if not versiontuple(np.__version__) >= versiontuple('1.9.0'):
X_test, y_test = X[list(test_idx), :], y[list(test_idx)]
warnings.warn('Please update to NumPy 1.9.0 or newer')
else:
X_test, y_test = X[test_idx, :], y[test_idx]
plt.scatter(
X_test[:, 0],
X_test[:, 1],
c='',
alpha=1.0,
linewidths=1,
marker='o',
s=55,
label='test set'
)
# generate sample data
np.random.seed(0)
X_xor = np.random.randn(200, 2)
y_xor = np.logical_xor(
X_xor[:, 0] > 0,
X_xor[:, 1] > 0
)
y_xor = np.where(y_xor, 1, -1)
Note: concepts on this page, have been integrated into the mlxtend library.
Penalty (C=1)¶
# create SVC classifier
svm = SVC(kernel='rbf', random_state=0, gamma=.01, C=1)
# train classifier
svm.fit(X_xor, y_xor)
# visualize decision boundaries
plot_decision_regions(X_xor, y_xor, classifier=svm)
plt.legend(loc='upper left')
plt.tight_layout()
plt.show()
Penalty (C=10)¶
# create SVC classifier
svm = SVC(kernel='rbf', random_state=0, gamma=.01, C=10)
# train classifier
svm.fit(X_xor, y_xor)
# visualize decision boundaries
plot_decision_regions(X_xor, y_xor, classifier=svm)
plt.legend(loc='upper left')
plt.tight_layout()
plt.show()
Penalty (C=10000)¶
# create SVC classifier
svm = SVC(kernel='rbf', random_state=0, gamma=.01, C=10000)
# train classifier
svm.fit(X_xor, y_xor)
# visualize decision boundaries
plot_decision_regions(X_xor, y_xor, classifier=svm)
plt.legend(loc='upper left')
plt.tight_layout()
plt.show()