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<li><a class="reference internal" href="#">Plot multi-class SGD on the iris dataset</a></li>
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<div class="section" id="plot-multi-class-sgd-on-the-iris-dataset">
<span id="example-linear-model-plot-sgd-iris-py"></span><h1>Plot multi-class SGD on the iris dataset<a class="headerlink" href="#plot-multi-class-sgd-on-the-iris-dataset" title="Permalink to this headline">ΒΆ</a></h1>
<p>Plot decision surface of multi-class SGD on iris dataset.
The hyperplanes corresponding to the three one-versus-all (OVA) classifiers
are represented by the dashed lines.</p>
<img alt="auto_examples/linear_model/images/plot_sgd_iris.png" class="align-center" src="auto_examples/linear_model/images/plot_sgd_iris.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_sgd_iris.py"><tt class="xref download docutils literal"><span class="pre">plot_sgd_iris.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><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="kn">from</span> <span class="nn">scikits.learn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">scikits.learn.linear_model</span> <span class="kn">import</span> <span class="n">SGDClassifier</span>
<span class="c"># import some data to play with</span>
<span class="n">iris</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span><span class="p">()</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="p">:</span><span class="mi">2</span><span class="p">]</span> <span class="c"># we only take the first two features. We could</span>
<span class="c"># avoid this ugly slicing by using a two-dim dataset</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span>
<span class="n">colors</span> <span class="o">=</span> <span class="s">"bry"</span>
<span class="c"># shuffle</span>
<span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">13</span><span class="p">)</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<span class="c"># standardize</span>
<span class="n">mean</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">std</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="p">(</span><span class="n">X</span> <span class="o">-</span> <span class="n">mean</span><span class="p">)</span> <span class="o">/</span> <span class="n">std</span>
<span class="n">h</span> <span class="o">=</span> <span class="o">.</span><span class="mo">02</span> <span class="c"># step size in the mesh</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">SGDClassifier</span><span class="p">(</span><span class="n">alpha</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c"># create a mesh to plot in</span>
<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">,</span> <span class="n">h</span><span class="p">),</span>
<span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span><span class="p">,</span> <span class="n">h</span><span class="p">))</span>
<span class="n">pl</span><span class="o">.</span><span class="n">set_cmap</span><span class="p">(</span><span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Paired</span><span class="p">)</span>
<span class="c"># Plot the decision boundary. For that, we will asign a color to each</span>
<span class="c"># point in the mesh [x_min, m_max]x[y_min, y_max].</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
<span class="c"># Put the result into a color plot</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">set_cmap</span><span class="p">(</span><span class="n">pl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Paired</span><span class="p">)</span>
<span class="n">cs</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">contourf</span><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">Z</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">'tight'</span><span class="p">)</span>
<span class="c"># Plot also the training points</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">color</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">classes</span><span class="p">,</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">y</span> <span class="o">==</span> <span class="n">i</span><span class="p">)</span>
<span class="n">pl</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">idx</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[</span><span class="n">idx</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">iris</span><span class="o">.</span><span class="n">target_names</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="n">pl</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Decision surface of multi-class SGD"</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">'tight'</span><span class="p">)</span>
<span class="c"># Plot the three one-against-all classifiers</span>
<span class="n">xmin</span><span class="p">,</span> <span class="n">xmax</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">xlim</span><span class="p">()</span>
<span class="n">ymin</span><span class="p">,</span> <span class="n">ymax</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">ylim</span><span class="p">()</span>
<span class="n">coef</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">coef_</span>
<span class="n">intercept</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">intercept_</span>
<span class="k">def</span> <span class="nf">plot_hyperplane</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">color</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">line</span><span class="p">(</span><span class="n">x0</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x0</span> <span class="o">*</span> <span class="n">coef</span><span class="p">[</span><span class="n">c</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">intercept</span><span class="p">[</span><span class="n">c</span><span class="p">])</span> <span class="o">/</span> <span class="n">coef</span><span class="p">[</span><span class="n">c</span><span class="p">,</span> <span class="mi">1</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">xmin</span><span class="p">,</span> <span class="n">xmax</span><span class="p">],</span> <span class="p">[</span><span class="n">line</span><span class="p">(</span><span class="n">xmin</span><span class="p">),</span> <span class="n">line</span><span class="p">(</span><span class="n">xmax</span><span class="p">)],</span>
<span class="n">ls</span><span class="o">=</span><span class="s">"--"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">color</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">classes</span><span class="p">,</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">plot_hyperplane</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">color</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">show</span><span class="p">()</span>
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