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<li><a class="reference internal" href="#">GMM Initialization Methods</a></li>
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<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-mixture-plot-gmm-init-py"><span class="std std-ref">here</span></a>
to download the full example code or to run this example in your browser via Binder</p>
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<section class="sphx-glr-example-title" id="gmm-initialization-methods">
<span id="sphx-glr-auto-examples-mixture-plot-gmm-init-py"></span><h1>GMM Initialization Methods<a class="headerlink" href="#gmm-initialization-methods" title="Permalink to this heading">¶</a></h1>
<p>Examples of the different methods of initialization in Gaussian Mixture Models</p>
<p>See <a class="reference internal" href="../../modules/mixture.html#gmm"><span class="std std-ref">Gaussian mixture models</span></a> for more information on the estimator.</p>
<p>Here we generate some sample data with four easy to identify clusters. The
purpose of this example is to show the four different methods for the
initialization parameter <em>init_param</em>.</p>
<p>The four initializations are <em>kmeans</em> (default), <em>random</em>, <em>random_from_data</em> and
<em>k-means++</em>.</p>
<p>Orange diamonds represent the initialization centers for the gmm generated by
the <em>init_param</em>. The rest of the data is represented as crosses and the
colouring represents the eventual associated classification after the GMM has
finished.</p>
<p>The numbers in the top right of each subplot represent the number of
iterations taken for the GaussianMixture to converge and the relative time
taken for the initialization part of the algorithm to run. The shorter
initialization times tend to have a greater number of iterations to converge.</p>
<p>The initialization time is the ratio of the time taken for that method versus
the time taken for the default <em>kmeans</em> method. As you can see all three
alternative methods take less time to initialize when compared to <em>kmeans</em>.</p>
<p>In this example, when initialized with <em>random_from_data</em> or <em>random</em> the model takes
more iterations to converge. Here <em>k-means++</em> does a good job of both low
time to initialize and low number of GaussianMixture iterations to converge.</p>
<img src="../../_images/sphx_glr_plot_gmm_init_001.png" srcset="../../_images/sphx_glr_plot_gmm_init_001.png" alt="GMM iterations and relative time taken to initialize, kmeans, Iter 9 | Init Time 1.00x, random_from_data, Iter 132 | Init Time 0.53x, k-means++, Iter 12 | Init Time 0.72x, random, Iter 56 | Init Time 0.48x" class = "sphx-glr-single-img"/><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Gordon Walsh <[email protected]></span>
<span class="c1"># Data generation code from Jake Vanderplas <[email protected]></span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">sklearn.mixture</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture" title="sklearn.mixture.GaussianMixture" class="sphx-glr-backref-module-sklearn-mixture sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GaussianMixture</span></a>
<span class="kn">from</span> <span class="nn">sklearn.utils.extmath</span> <span class="kn">import</span> <span class="n">row_norms</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets._samples_generator</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_blobs.html#sklearn.datasets.make_blobs" title="sklearn.datasets.make_blobs" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_blobs</span></a>
<span class="kn">from</span> <span class="nn">timeit</span> <span class="kn">import</span> <span class="n">default_timer</span> <span class="k">as</span> <a href="https://docs.python.org/3/library/timeit.html#timeit.default_timer" title="timeit.default_timer" class="sphx-glr-backref-module-timeit sphx-glr-backref-type-py-function"><span class="n">timer</span></a>
<span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="c1"># Generate some data</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y_true</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_blobs.html#sklearn.datasets.make_blobs" title="sklearn.datasets.make_blobs" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_blobs</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">4000</span><span class="p">,</span> <span class="n">centers</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">cluster_std</span><span class="o">=</span><span class="mf">0.60</span><span class="p">,</span> <span class="n">random_state</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="n">X</span><span class="p">[:,</span> <span class="p">::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">4000</span>
<span class="n">n_components</span> <span class="o">=</span> <span class="mi">4</span>
<span class="n">x_squared_norms</span> <span class="o">=</span> <span class="n">row_norms</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">squared</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">get_initial_means</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">init_params</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>
<span class="c1"># Run a GaussianMixture with max_iter=0 to output the initalization means</span>
<span class="n">gmm</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture" title="sklearn.mixture.GaussianMixture" class="sphx-glr-backref-module-sklearn-mixture sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GaussianMixture</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">init_params</span><span class="o">=</span><span class="n">init_params</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">r</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="k">return</span> <span class="n">gmm</span><span class="o">.</span><span class="n">means_</span>
<span class="n">methods</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"kmeans"</span><span class="p">,</span> <span class="s2">"random_from_data"</span><span class="p">,</span> <span class="s2">"k-means++"</span><span class="p">,</span> <span class="s2">"random"</span><span class="p">]</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"navy"</span><span class="p">,</span> <span class="s2">"turquoise"</span><span class="p">,</span> <span class="s2">"cornflowerblue"</span><span class="p">,</span> <span class="s2">"darkorange"</span><span class="p">]</span>
<span class="n">times_init</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">relative_times</span> <span class="o">=</span> <span class="p">{}</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">methods</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span>
<span class="n">bottom</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mf">0.15</span><span class="p">,</span> <span class="n">wspace</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">left</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mf">0.95</span>
<span class="p">)</span>
<span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">method</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">methods</span><span class="p">):</span>
<span class="n">r</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/random/legacy.html#numpy.random.RandomState" title="numpy.random.RandomState" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span></a><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="mi">1234</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">methods</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">start</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/timeit.html#timeit.default_timer" title="timeit.default_timer" class="sphx-glr-backref-module-timeit sphx-glr-backref-type-py-function"><span class="n">timer</span></a><span class="p">()</span>
<span class="n">ini</span> <span class="o">=</span> <span class="n">get_initial_means</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">method</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<span class="n">end</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/timeit.html#timeit.default_timer" title="timeit.default_timer" class="sphx-glr-backref-module-timeit sphx-glr-backref-type-py-function"><span class="n">timer</span></a><span class="p">()</span>
<span class="n">init_time</span> <span class="o">=</span> <span class="n">end</span> <span class="o">-</span> <span class="n">start</span>
<span class="n">gmm</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.mixture.GaussianMixture.html#sklearn.mixture.GaussianMixture" title="sklearn.mixture.GaussianMixture" class="sphx-glr-backref-module-sklearn-mixture sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">GaussianMixture</span></a><span class="p">(</span>
<span class="n">n_components</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">means_init</span><span class="o">=</span><span class="n">ini</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-9</span><span class="p">,</span> <span class="n">max_iter</span><span class="o">=</span><span class="mi">2000</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="n">r</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">times_init</span><span class="p">[</span><span class="n">method</span><span class="p">]</span> <span class="o">=</span> <span class="n">init_time</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">enumerate</span><span class="p">(</span><span class="n">colors</span><span class="p">):</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">gmm</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="o">==</span> <span class="n">i</span><span class="p">]</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">data</span><span class="p">[:,</span> <span class="mi">1</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">marker</span><span class="o">=</span><span class="s2">"x"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html#matplotlib.pyplot.scatter" title="matplotlib.pyplot.scatter" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">scatter</span></a><span class="p">(</span>
<span class="n">ini</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">ini</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">75</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"D"</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">"orange"</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mf">1.5</span><span class="p">,</span> <span class="n">edgecolors</span><span class="o">=</span><span class="s2">"black"</span>
<span class="p">)</span>
<span class="n">relative_times</span><span class="p">[</span><span class="n">method</span><span class="p">]</span> <span class="o">=</span> <span class="n">times_init</span><span class="p">[</span><span class="n">method</span><span class="p">]</span> <span class="o">/</span> <span class="n">times_init</span><span class="p">[</span><span class="n">methods</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="n">method</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">"left"</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span>
<span class="s2">"Iter </span><span class="si">%i</span><span class="s2"> | Init Time </span><span class="si">%.2f</span><span class="s2">x"</span> <span class="o">%</span> <span class="p">(</span><span class="n">gmm</span><span class="o">.</span><span class="n">n_iter_</span><span class="p">,</span> <span class="n">relative_times</span><span class="p">[</span><span class="n">method</span><span class="p">]),</span>
<span class="n">loc</span><span class="o">=</span><span class="s2">"right"</span><span class="p">,</span>
<span class="n">fontsize</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="matplotlib.pyplot.suptitle" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="s2">"GMM iterations and relative time taken to initialize"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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