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()
svm penalty c=1

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()
svm penalty c=10

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()
svm penalty c=10000