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<div class="section" id="gaussian-mixture-model-ellipsoids">
<span id="example-mixture-plot-gmm-py"></span><h1>Gaussian Mixture Model Ellipsoids<a class="headerlink" href="#gaussian-mixture-model-ellipsoids" title="Permalink to this headline">ΒΆ</a></h1>
<p>Plot the confidence ellipsoids of a mixture of two gaussians.</p>
<img alt="auto_examples/mixture/images/plot_gmm.png" class="align-center" src="auto_examples/mixture/images/plot_gmm.png" />
<p><strong>Python source code:</strong> <a class="reference download internal" href="../../_downloads/plot_gmm.py"><tt class="xref download docutils literal"><span class="pre">plot_gmm.py</span></tt></a></p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scikits.learn</span> <span class="kn">import</span> <span class="n">mixture</span>
<span class="kn">import</span> <span class="nn">itertools</span>
<span class="kn">import</span> <span class="nn">pylab</span> <span class="kn">as</span> <span class="nn">pl</span>
<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="kn">as</span> <span class="nn">mpl</span>
<span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="mi">2</span>
<span class="c"># generate random sample, two components</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">0</span><span class="p">)</span>
<span class="n">C</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.7</span><span class="p">],</span> <span class="p">[</span><span class="mf">3.5</span><span class="p">,</span> <span class="o">.</span><span class="mi">7</span><span class="p">]])</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">dot</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">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">C</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">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">])]</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">mixture</span><span class="o">.</span><span class="n">GMM</span><span class="p">(</span><span class="n">n_states</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">cvtype</span><span class="o">=</span><span class="s">'full'</span><span class="p">)</span>
<span class="n">clf</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">splot</span> <span class="o">=</span> <span class="n">pl</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s">'equal'</span><span class="p">)</span>
<span class="n">color_iter</span> <span class="o">=</span> <span class="n">itertools</span><span class="o">.</span><span class="n">cycle</span> <span class="p">([</span><span class="s">'r'</span><span class="p">,</span> <span class="s">'g'</span><span class="p">,</span> <span class="s">'b'</span><span class="p">,</span> <span class="s">'c'</span><span class="p">])</span>
<span class="n">Y_</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">X</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="n">covar</span><span class="p">,</span> <span class="n">color</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">clf</span><span class="o">.</span><span class="n">means</span><span class="p">,</span> <span class="n">clf</span><span class="o">.</span><span class="n">covars</span><span class="p">,</span> <span class="n">color_iter</span><span class="p">)):</span>
<span class="n">v</span><span class="p">,</span> <span class="n">w</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eigh</span><span class="p">(</span><span class="n">covar</span><span class="p">)</span>
<span class="n">u</span> <span class="o">=</span> <span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">w</span><span class="p">[</span><span class="mi">0</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">Y_</span><span class="o">==</span><span class="n">i</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">Y_</span><span class="o">==</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="o">.</span><span class="mi">8</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="n">angle</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">angle</span> <span class="o">=</span> <span class="mi">180</span> <span class="o">*</span> <span class="n">angle</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="c"># convert to degrees</span>
<span class="n">ell</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">patches</span><span class="o">.</span><span class="n">Ellipse</span> <span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">180</span> <span class="o">+</span> <span class="n">angle</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="n">ell</span><span class="o">.</span><span class="n">set_clip_box</span><span class="p">(</span><span class="n">splot</span><span class="o">.</span><span class="n">bbox</span><span class="p">)</span>
<span class="n">ell</span><span class="o">.</span><span class="n">set_alpha</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">splot</span><span class="o">.</span><span class="n">add_artist</span><span class="p">(</span><span class="n">ell</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>
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