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class="documentwrapper"> <div class="bodywrapper"> <div class="body"> <div class="section" id="sgd-penalties"> <span id="example-linear-model-plot-sgd-penalties-py"></span><h1>SGD: Penalties<a class="headerlink" href="#sgd-penalties" title="Permalink to this headline">ΒΆ</a></h1> <p>Plot the contours of the three penalties supported by <cite>scikits.learn.linear_model.stochastic_gradient</cite>.</p> <img alt="../../_images/plot_sgd_penalties.png" class="align-center" src="../../_images/plot_sgd_penalties.png" /> <p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_sgd_penalties.py"><tt class="xref download docutils literal"><span class="pre">plot_sgd_penalties.py</span></tt></a></p> <div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span> <span class="k">print</span> <span class="n">__doc__</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">pylab</span> <span class="kn">as</span> <span class="nn">pl</span> <span class="k">def</span> <span class="nf">l1</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mf">2.0</span><span class="p">))</span><span class="o">**</span><span class="mf">2.0</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xs</span><span class="p">])</span> <span class="k">def</span> <span class="nf">l2</span><span class="p">(</span><span class="n">xs</span><span class="p">):</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="n">x</span><span class="o">**</span><span class="mf">2.0</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xs</span><span class="p">])</span> <span class="k">def</span> <span class="nf">el</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([(</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">z</span> <span class="o">+</span> <span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">z</span> <span class="o">-</span> <span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">8</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">8</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">16</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">8</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">z</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">4</span><span class="o">*</span><span class="n">z</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xs</span><span class="p">])</span> <span class="k">def</span> <span class="nf">cross</span><span class="p">(</span><span class="n">ext</span><span class="p">):</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="o">-</span><span class="n">ext</span><span class="p">,</span><span class="n">ext</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s">"k-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="n">ext</span><span class="p">,</span><span class="n">ext</span><span class="p">],</span> <span class="s">"k-"</span><span class="p">)</span> <span class="n">xs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.501</span> <span class="c"># 0.5 division throuh zero</span> <span class="n">cross</span><span class="p">(</span><span class="mf">1.2</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">l1</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"r-"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"L1"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="o">*</span><span class="n">l1</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"r-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="n">l1</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"r-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="o">*</span><span class="n">l1</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"r-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">l2</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"b-"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"L2"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="n">l2</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"b-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="n">l2</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"b-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="n">l2</span><span class="p">(</span><span class="n">xs</span><span class="p">),</span> <span class="s">"b-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">el</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">alpha</span><span class="p">),</span> <span class="s">"y-"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s">"Elastic Net"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="n">el</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">alpha</span><span class="p">),</span> <span class="s">"y-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="n">el</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">alpha</span><span class="p">),</span> <span class="s">"y-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="n">xs</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span> <span class="o">*</span> <span class="n">el</span><span class="p">(</span><span class="n">xs</span><span class="p">,</span> <span class="n">alpha</span><span class="p">),</span> <span class="s">"y-"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">r"$w_0$"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">r"$w_1$"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span> <span class="n">pl</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s">"equal"</span><span class="p">)</span> <span class="n">pl</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </pre></div> </div> </div> </div> </div> </div> <div class="clearer"></div> </div> </div> <div class="footer"> <p style="text-align: center">This documentation is relative to scikits.learn version 0.6.0<p> © 2010, scikits.learn developers (BSD Lincense). 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