Show Sidebar Hide Sidebar

SGD Penalties in Scikit-learn

Plot the contours of the three penalties.

All of the above are supported by sklearn.linear_model.stochastic_gradient.

New to Plotly?

Plotly's Python library is free and open source! Get started by downloading the client and reading the primer.
You can set up Plotly to work in online or offline mode, or in jupyter notebooks.
We also have a quick-reference cheatsheet (new!) to help you get started!

Version

In [1]:
import sklearn
sklearn.__version__
Out[1]:
'0.18.1'

Imports

In [2]:
import plotly.plotly as py
import plotly.graph_objs as go

from __future__ import division
import numpy as np

Calculations

In [3]:
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):
    p1 = go.Scatter(x=[-ext, ext], y=[0, 0], 
                    mode='lines', line=dict(color='black', width=1),
                    showlegend=False)
    p2 = go.Scatter(x=[0, 0], y=[-ext, ext],
                    mode='lines', line=dict(color='black', width=1),
                    showlegend=False)
    return [p1, p2]
In [4]:
xs = np.linspace(0, 1, 100)

alpha = 0.501  # 0.5 division throuh zero

data = cross(1.2)

l1_color = "cyan"
l2_color = "blue"
elastic_net_color = "orange"
lw = 2
In [5]:
p1 = go.Scatter(x=xs, y=l1(xs),
                mode='lines',
                line=dict(color=l1_color, width=lw),
                name="L1")
data.append(p1)

p2 = go.Scatter(x=xs, y=-1.0 * l1(xs), 
                mode='lines',
                line=dict(color=l1_color, width=lw),
                showlegend=False)
data.append(p2)

p3 = go.Scatter(x=-1 * xs, y=l1(xs), 
                mode='lines',
                line=dict(color=l1_color, width=lw),
                showlegend=False)
data.append(p3)

p4 = go.Scatter(x=-1 * xs, y=-1.0 * l1(xs), 
                mode='lines',
                line=dict(color=l1_color, width=lw),
                showlegend=False)
data.append(p4)

p5 = go.Scatter(x=xs, y=l2(xs),
                mode='lines',
                line=dict(color=l2_color, width=lw),
                name='L2')
data.append(p5)

p6 = go.Scatter(x=xs, y=-1.0 * l2(xs), 
                mode='lines',
                line=dict(color=l2_color, width=lw),
                showlegend=False)
data.append(p6)

p7 = go.Scatter(x=-1 * xs, y=l2(xs),
                mode='lines',
                line=dict(color=l2_color, width=lw),
                showlegend=False)
data.append(p7)

p8 = go.Scatter(x=-1 * xs, y=-1.0 * l2(xs),
                mode='lines',
                line=dict(color=l2_color, width=lw),
                showlegend=False) 
data.append(p8)

p9 = go.Scatter(x=xs, y=el(xs, alpha), 
                mode='lines',
                line=dict(color=elastic_net_color, width=lw),
                name="Elastic Net")
data.append(p9)

p10 = go.Scatter(x=xs, y=-1.0 * el(xs, alpha), 
                mode='lines',
                line=dict(color=elastic_net_color, width=lw),
                showlegend=False)
data.append(p10)

p11 = go.Scatter(x=-1 * xs, y=el(xs, alpha), 
                mode='lines',
                line=dict(color=elastic_net_color, width=lw),
                showlegend=False)
data.append(p11)

p12 = go.Scatter(x=-1 * xs, y=-1.0 * el(xs, alpha),
                mode='lines',
                line=dict(color=elastic_net_color, width=lw),
                showlegend=False)
data.append(p12)

layout = go.Layout(xaxis=dict(title='w<sub>0</sub>', 
                              zeroline=False, showgrid=False),
                   yaxis=dict(title='w<sub>1</sub>',
                              zeroline=False, showgrid=False),
                   hovermode='closest'
                  )
fig = go.Figure(data=data, layout=layout)
Still need help?
Contact Us

For guaranteed 24 hour response turnarounds, upgrade to a Developer Support Plan.