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<div class="section" id="density-estimation-for-a-gaussian-mixture">
<span id="sphx-glr-auto-examples-mixture-plot-gmm-pdf-py"></span><h1>Density Estimation for a Gaussian mixture<a class="headerlink" href="#density-estimation-for-a-gaussian-mixture" title="Permalink to this headline">¶</a></h1>
<p>Plot the density estimation of a mixture of two Gaussians. Data is
generated from two Gaussians with different centers and covariance
matrices.</p>
<img alt="../../_images/sphx_glr_plot_gmm_pdf_001.png" class="align-center" src="../../_images/sphx_glr_plot_gmm_pdf_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></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">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib.colors</span> <span class="kn">import</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.colors.LogNorm.html#matplotlib.colors.LogNorm" title="View documentation for matplotlib.colors.LogNorm"><span class="n">LogNorm</span></a>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">mixture</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">300</span>
<span class="c1"># generate random sample, two components</span>
<a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.seed.html#numpy.random.seed" title="View documentation for numpy.random.seed"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<span class="c1"># generate spherical data centered on (20, 20)</span>
<span class="n">shifted_gaussian</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.randn.html#numpy.random.randn" title="View documentation for numpy.random.randn"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="mi">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">])</span>
<span class="c1"># generate zero centered stretched Gaussian data</span>
<span class="n">C</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><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">stretched_gaussian</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.dot.html#numpy.dot" title="View documentation for numpy.dot"><span class="n">np</span><span class="o">.</span><span class="n">dot</span></a><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.randn.html#numpy.random.randn" title="View documentation for numpy.random.randn"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="n">n_samples</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="c1"># concatenate the two datasets into the final training set</span>
<span class="n">X_train</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.vstack.html#numpy.vstack" title="View documentation for numpy.vstack"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">([</span><span class="n">shifted_gaussian</span><span class="p">,</span> <span class="n">stretched_gaussian</span><span class="p">])</span>
<span class="c1"># fit a Gaussian Mixture Model with two components</span>
<span class="n">clf</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture" title="View documentation for sklearn.mixture.GaussianMixture"><span class="n">mixture</span><span class="o">.</span><span class="n">GaussianMixture</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">covariance_type</span><span class="o">=</span><span class="s1">'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_train</span><span class="p">)</span>
<span class="c1"># display predicted scores by the model as a contour plot</span>
<span class="n">x</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">20.</span><span class="p">,</span> <span class="mf">30.</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">20.</span><span class="p">,</span> <span class="mf">40.</span><span class="p">)</span>
<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/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">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">XX</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="n">X</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">Y</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span><span class="o">.</span><span class="n">T</span>
<span class="n">Z</span> <span class="o">=</span> <span class="o">-</span><span class="n">clf</span><span class="o">.</span><span class="n">score_samples</span><span class="p">(</span><span class="n">XX</span><span class="p">)</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">X</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">CS</span> <span class="o">=</span> <a href="http://matplotlib.org/api/contour_api.html#matplotlib.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">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><a href="http://matplotlib.org/api/_as_gen/matplotlib.colors.LogNorm.html#matplotlib.colors.LogNorm" title="View documentation for matplotlib.colors.LogNorm"><span class="n">LogNorm</span></a><span class="p">(</span><span class="n">vmin</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
<span class="n">levels</span><span class="o">=</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.logspace.html#numpy.logspace" title="View documentation for numpy.logspace"><span class="n">np</span><span class="o">.</span><span class="n">logspace</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">CB</span> <span class="o">=</span> <a href="http://matplotlib.org/api/colorbar_api.html#matplotlib.colorbar" title="View documentation for matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">CS</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">extend</span><span class="o">=</span><span class="s1">'both'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="View documentation for matplotlib.pyplot.scatter"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">X_train</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_train</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>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="View documentation for matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Negative log-likelihood predicted by a GMM'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/axis_api.html#matplotlib.axis" title="View documentation for matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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