3D plot of making a 2D non-linearly-seperable problem (XOR) into a 3D linearly seperable one with feature mapping.

xor.py

from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# original data
# not linearly separable in 2D
x = np.array([[1, 1], [-1, -1], [-1, 1], [1, -1]])
y = np.array([-1, -1, 1, 1])

# feature mapping to produce x3 = x1 | x2
# add feature x3            | x3 computed here |
x = np.hstack([x, np.array([x[:, 0] | x[:, 1]]).T])
plus = x[y == 1]
minus = x[y == -1]
ax.scatter(plus[:, 0], plus[:, 1], plus[:, 2], c='b')
ax.scatter(minus[:, 0], minus[:, 1], minus[:, 2], c='r')

# these control the position and norm of the plane
point  = np.array([0, 0, 0.5])
normal = np.array([-1, -1, 2])

# this is copy paste for plotting a plane
# a plane is a*x+b*y+c*z+d=0
# [a,b,c] is the normal. Thus, we have to calculate
# d and we're set
d = -point.dot(normal)
xx, yy = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
# calculate corresponding z
z = (-normal[0] * xx - normal[1] * yy + d) * 1. /normal[2]
# plot the surface
ax.plot_surface(xx, yy, z, alpha=0.4)
plt.show()