Solving non-linear problems using a kernel SVM

1. Create a simple dataset that has the form of an XOR gate using the logical_xor function from NumPy .

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)

2. Show created dataset

plt.scatter(X_xor[y_xor == 1, 0],
            X_xor[y_xor == 1, 1],
            c='b', marker='x',
            label='1')
plt.scatter(X_xor[y_xor == -1, 0],
            X_xor[y_xor == -1, 1],
            c='r',
            marker='s',
            label='-1')

plt.xlim([-3, 3])
plt.ylim([-3, 3])
plt.legend(loc='best')
plt.show()

3.  Using the kernel trick to fnd separating hyperplanes in higher dimensional space

svm = SVC(kernel='rbf', random_state=0, gamma=0.10, C=10.0)
svm.fit(X_xor, y_xor)

4.  Show Results

plot_decision_regions(X_xor, y_xor,
                      classifier=svm)

plt.legend(loc='upper left')
plt.show()

Reference ：《Python Machine Learning》