68 lines
1.5 KiB
Python
68 lines
1.5 KiB
Python
"""
|
|
==============
|
|
SGD: Penalties
|
|
==============
|
|
|
|
Plot the contours of the three penalties.
|
|
|
|
All of the above are supported by
|
|
:class:`sklearn.linear_model.stochastic_gradient`.
|
|
|
|
"""
|
|
from __future__ import division
|
|
print(__doc__)
|
|
|
|
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
|
|
|
|
def l1(xs):
|
|
return np.array([np.sqrt((1 - np.sqrt(x ** 2.0)) ** 2.0) for x in xs])
|
|
|
|
|
|
def l2(xs):
|
|
return np.array([np.sqrt(1.0 - x ** 2.0) for x in xs])
|
|
|
|
|
|
def el(xs, z):
|
|
return np.array([(2 - 2 * x - 2 * z + 4 * x * z -
|
|
(4 * z ** 2
|
|
- 8 * x * z ** 2
|
|
+ 8 * x ** 2 * z ** 2
|
|
- 16 * x ** 2 * z ** 3
|
|
+ 8 * x * z ** 3 + 4 * x ** 2 * z ** 4) ** (1. / 2)
|
|
- 2 * x * z ** 2) / (2 - 4 * z) for x in xs])
|
|
|
|
|
|
def cross(ext):
|
|
plt.plot([-ext, ext], [0, 0], "k-")
|
|
plt.plot([0, 0], [-ext, ext], "k-")
|
|
|
|
xs = np.linspace(0, 1, 100)
|
|
|
|
alpha = 0.501 # 0.5 division throuh zero
|
|
|
|
cross(1.2)
|
|
|
|
plt.plot(xs, l1(xs), "r-", label="L1")
|
|
plt.plot(xs, -1.0 * l1(xs), "r-")
|
|
plt.plot(-1 * xs, l1(xs), "r-")
|
|
plt.plot(-1 * xs, -1.0 * l1(xs), "r-")
|
|
|
|
plt.plot(xs, l2(xs), "b-", label="L2")
|
|
plt.plot(xs, -1.0 * l2(xs), "b-")
|
|
plt.plot(-1 * xs, l2(xs), "b-")
|
|
plt.plot(-1 * xs, -1.0 * l2(xs), "b-")
|
|
|
|
plt.plot(xs, el(xs, alpha), "y-", label="Elastic Net")
|
|
plt.plot(xs, -1.0 * el(xs, alpha), "y-")
|
|
plt.plot(-1 * xs, el(xs, alpha), "y-")
|
|
plt.plot(-1 * xs, -1.0 * el(xs, alpha), "y-")
|
|
|
|
plt.xlabel(r"$w_0$")
|
|
plt.ylabel(r"$w_1$")
|
|
plt.legend()
|
|
|
|
plt.axis("equal")
|
|
plt.show()
|