1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
|
"""
==============
SGD: Penalties
==============
Plot the contours of the three penalties supported by
`sklearn.linear_model.stochastic_gradient`.
"""
from __future__ import division
print __doc__
import numpy as np
import pylab as pl
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):
pl.plot([-ext, ext], [0, 0], "k-")
pl.plot([0, 0], [-ext, ext], "k-")
xs = np.linspace(0, 1, 100)
alpha = 0.501 # 0.5 division throuh zero
cross(1.2)
pl.plot(xs, l1(xs), "r-", label="L1")
pl.plot(xs, -1.0 * l1(xs), "r-")
pl.plot(-1 * xs, l1(xs), "r-")
pl.plot(-1 * xs, -1.0 * l1(xs), "r-")
pl.plot(xs, l2(xs), "b-", label="L2")
pl.plot(xs, -1.0 * l2(xs), "b-")
pl.plot(-1 * xs, l2(xs), "b-")
pl.plot(-1 * xs, -1.0 * l2(xs), "b-")
pl.plot(xs, el(xs, alpha), "y-", label="Elastic Net")
pl.plot(xs, -1.0 * el(xs, alpha), "y-")
pl.plot(-1 * xs, el(xs, alpha), "y-")
pl.plot(-1 * xs, -1.0 * el(xs, alpha), "y-")
pl.xlabel(r"$w_0$")
pl.ylabel(r"$w_1$")
pl.legend()
pl.axis("equal")
pl.show()
|
