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<span id="sphx-glr-auto-examples-linear-model-plot-sgd-penalties-py"></span><h1>SGD: Penalties<a class="headerlink" href="#sgd-penalties" title="Permalink to this headline">¶</a></h1>
<p>Contours of where the penalty is equal to 1
for the three penalties L1, L2 and elastic-net.</p>
<p>All of the above are supported by
<code class="xref py py-class docutils literal"><span class="pre">sklearn.linear_model.stochastic_gradient</span></code>.</p>
<img alt="../../_images/sphx_glr_plot_sgd_penalties_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_sgd_penalties_001.png" />
<p class="sphx-glr-script-out">Out:</p>
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</pre></div>
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<div class="line"><br /></div>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="n">l1_color</span> <span class="o">=</span> <span class="s2">"navy"</span>
<span class="n">l2_color</span> <span class="o">=</span> <span class="s2">"c"</span>
<span class="n">elastic_net_color</span> <span class="o">=</span> <span class="s2">"darkorange"</span>
<span class="n">line</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html#numpy.linspace" title="View documentation for numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mi">1001</span><span class="p">)</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">line</span><span class="p">,</span> <span class="n">line</span><span class="p">)</span>
<span class="n">l2</span> <span class="o">=</span> <span class="n">xx</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">yy</span> <span class="o">**</span> <span class="mi">2</span>
<span class="n">l1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">xx</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">yy</span><span class="p">)</span>
<span class="n">rho</span> <span class="o">=</span> <span class="mf">0.5</span>
<span class="n">elastic_net</span> <span class="o">=</span> <span class="n">rho</span> <span class="o">*</span> <span class="n">l1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">rho</span><span class="p">)</span> <span class="o">*</span> <span class="n">l2</span>
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<span class="n">ax</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.gca.html#matplotlib.pyplot.gca" title="View documentation for matplotlib.pyplot.gca"><span class="n">plt</span><span class="o">.</span><span class="n">gca</span></a><span class="p">()</span>
<span class="n">elastic_net_contour</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="View documentation for matplotlib.pyplot.contour"><span class="n">plt</span><span class="o">.</span><span class="n">contour</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">elastic_net</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
<span class="n">colors</span><span class="o">=</span><span class="n">elastic_net_color</span><span class="p">)</span>
<span class="n">l2_contour</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="View documentation for matplotlib.pyplot.contour"><span class="n">plt</span><span class="o">.</span><span class="n">contour</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">l2</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="n">l2_color</span><span class="p">)</span>
<span class="n">l1_contour</span> <span class="o">=</span> <a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="View documentation for matplotlib.pyplot.contour"><span class="n">plt</span><span class="o">.</span><span class="n">contour</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">l1</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">colors</span><span class="o">=</span><span class="n">l1_color</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'left'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">(</span><span class="s1">'center'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'right'</span><span class="p">]</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s1">'none'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'bottom'</span><span class="p">]</span><span class="o">.</span><span class="n">set_position</span><span class="p">(</span><span class="s1">'center'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">spines</span><span class="p">[</span><span class="s1">'top'</span><span class="p">]</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s1">'none'</span><span class="p">)</span>
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<span class="n">fmt</span><span class="o">=</span><span class="p">{</span><span class="mf">1.0</span><span class="p">:</span> <span class="s1">'elastic-net'</span><span class="p">},</span> <span class="n">manual</span><span class="o">=</span><span class="p">[(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)])</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.clabel.html#matplotlib.pyplot.clabel" title="View documentation for matplotlib.pyplot.clabel"><span class="n">plt</span><span class="o">.</span><span class="n">clabel</span></a><span class="p">(</span><span class="n">l2_contour</span><span class="p">,</span> <span class="n">inline</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">18</span><span class="p">,</span>
<span class="n">fmt</span><span class="o">=</span><span class="p">{</span><span class="mf">1.0</span><span class="p">:</span> <span class="s1">'L2'</span><span class="p">},</span> <span class="n">manual</span><span class="o">=</span><span class="p">[(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)])</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.clabel.html#matplotlib.pyplot.clabel" title="View documentation for matplotlib.pyplot.clabel"><span class="n">plt</span><span class="o">.</span><span class="n">clabel</span></a><span class="p">(</span><span class="n">l1_contour</span><span class="p">,</span> <span class="n">inline</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">18</span><span class="p">,</span>
<span class="n">fmt</span><span class="o">=</span><span class="p">{</span><span class="mf">1.0</span><span class="p">:</span> <span class="s1">'L1'</span><span class="p">},</span> <span class="n">manual</span><span class="o">=</span><span class="p">[(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)])</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="View documentation for matplotlib.pyplot.tight_layout"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
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