def perceptron(X, Y):
"""
Function to
a perceptron to the kernelized input data.
Parameters
----------
X: Numpy array with the input 2D data points [n_samples, 2]
Y: Numpy array with the binary classes (either 0 or 1) [n_samples,]
Returns
-------
is_linearly_separable: Boolean value indicating whether the data is
linearly separable or not
"""
is_linearly_separable = False
kernelX = kernelize(
X, Y) # Y is passed to plot the kernelized data with labels
"""
Create a Perceptron instance and fit it to the kernelized data.
For details on how to do this in scikit-learn, refer:
http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Perceptron.html
==========================================================================
"""
# YOUR CODE GOES HERE
m = Perceptron()
m.fit(kernelX, Y)
train_predictions = m.predict(kernelX)
train_labels = Y
clf = m.densify()
"""
==========================================================================
"""
"""
Calculates training accuracy. Replace predictions and labels with your
respective variable names.
"""
train_accuracy = calculate_accuracy(train_predictions, train_labels)
print "Training Accuracy: %.4f" % (train_accuracy)
if train_accuracy == 1:
is_linearly_separable = True
"""
Code to plot the 3D decision surface that separates the points. Visualization
will help in understanding how the kernel has performed.
"""
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
color = lambda x: 'r' if x else 'b'
mark = lambda x: 'o' if x else '^'
for i in range(kernelX.shape[0]):
x, y, z = kernelX[i]
ax.scatter(x, y, z, c=color(Y[i]), marker=mark(Y[i]))
W = clf.coef_[0] # 3D normal
intercept = clf.intercept_[0] # Distance from origin
xx, yy = np.meshgrid(kernelX[:, 0], kernelX[:, 1])
"""
Derived from a*x + b*y + c*z + d = 0. (a, b, c) is the normal and we know
x and y values. d is the distance from origin, or the intercept. Hence, value
of z => (-a*x - b*y - d) / c.
Source: https://stackoverflow.com/questions/3461869/plot-a-plane-based-on-a-normal-vector-and-a-point-in-matlab-or-matplotlib
"""
zz = ((-W[0] * xx) + (-W[1] * yy) + (-intercept)) * 1. / W[2]
ax.plot_surface(xx,
yy,
zz,
rstride=10,
cstride=10,
color='g',
antialiased=False,
linewidth=0,
shade=False)
plt.show()
return is_linearly_separable
