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<li><a class="reference internal" href="#">Demo of OPTICS clustering algorithm</a></li>
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<section class="sphx-glr-example-title" id="demo-of-optics-clustering-algorithm">
<span id="sphx-glr-auto-examples-cluster-plot-optics-py"></span><h1>Demo of OPTICS clustering algorithm<a class="headerlink" href="#demo-of-optics-clustering-algorithm" title="Link to this heading">¶</a></h1>
<p>Finds core samples of high density and expands clusters from them.
This example uses data that is generated so that the clusters have
different densities.</p>
<p>The <a class="reference internal" href="../../modules/generated/sklearn.cluster.OPTICS.html#sklearn.cluster.OPTICS" title="sklearn.cluster.OPTICS"><code class="xref py py-class docutils literal notranslate"><span class="pre">OPTICS</span></code></a> is first used with its Xi cluster detection
method, and then setting specific thresholds on the reachability, which
corresponds to <a class="reference internal" href="../../modules/generated/sklearn.cluster.DBSCAN.html#sklearn.cluster.DBSCAN" title="sklearn.cluster.DBSCAN"><code class="xref py py-class docutils literal notranslate"><span class="pre">DBSCAN</span></code></a>. We can see that the different
clusters of OPTICS’s Xi method can be recovered with different choices of
thresholds in DBSCAN.</p>
<img src="../../_images/sphx_glr_plot_optics_001.png" srcset="../../_images/sphx_glr_plot_optics_001.png" alt="Reachability Plot, Automatic Clustering OPTICS, Clustering at 0.5 epsilon cut DBSCAN, Clustering at 2.0 epsilon cut DBSCAN" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Authors: Shane Grigsby <[email protected]></span>
<span class="c1"># Adrin Jalali <[email protected]></span>
<span class="c1"># License: BSD 3 clause</span>
<span class="kn">import</span> <span class="nn">matplotlib.gridspec</span> <span class="k">as</span> <span class="nn">gridspec</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.cluster</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.cluster.OPTICS.html#sklearn.cluster.OPTICS" title="sklearn.cluster.OPTICS" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OPTICS</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.cluster.cluster_optics_dbscan.html#sklearn.cluster.cluster_optics_dbscan" title="sklearn.cluster.cluster_optics_dbscan" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-function"><span class="n">cluster_optics_dbscan</span></a>
<span class="c1"># Generate sample data</span>
<a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html#numpy.random.seed" title="numpy.random.seed" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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="n">n_points_per_cluster</span> <span class="o">=</span> <span class="mi">250</span>
<span class="n">C1</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.8</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">C2</span> <span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.1</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">C3</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.2</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">C4</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.3</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">C5</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mf">1.6</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">C6</span> <span class="o">=</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><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_points_per_cluster</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.vstack.html#numpy.vstack" title="numpy.vstack" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">vstack</span></a><span class="p">((</span><span class="n">C1</span><span class="p">,</span> <span class="n">C2</span><span class="p">,</span> <span class="n">C3</span><span class="p">,</span> <span class="n">C4</span><span class="p">,</span> <span class="n">C5</span><span class="p">,</span> <span class="n">C6</span><span class="p">))</span>
<span class="n">clust</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.OPTICS.html#sklearn.cluster.OPTICS" title="sklearn.cluster.OPTICS" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">OPTICS</span></a><span class="p">(</span><span class="n">min_samples</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">xi</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">min_cluster_size</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="c1"># Run the fit</span>
<span class="n">clust</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">labels_050</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.cluster_optics_dbscan.html#sklearn.cluster.cluster_optics_dbscan" title="sklearn.cluster.cluster_optics_dbscan" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-function"><span class="n">cluster_optics_dbscan</span></a><span class="p">(</span>
<span class="n">reachability</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">reachability_</span><span class="p">,</span>
<span class="n">core_distances</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">core_distances_</span><span class="p">,</span>
<span class="n">ordering</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">ordering_</span><span class="p">,</span>
<span class="n">eps</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">labels_200</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.cluster.cluster_optics_dbscan.html#sklearn.cluster.cluster_optics_dbscan" title="sklearn.cluster.cluster_optics_dbscan" class="sphx-glr-backref-module-sklearn-cluster sphx-glr-backref-type-py-function"><span class="n">cluster_optics_dbscan</span></a><span class="p">(</span>
<span class="n">reachability</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">reachability_</span><span class="p">,</span>
<span class="n">core_distances</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">core_distances_</span><span class="p">,</span>
<span class="n">ordering</span><span class="o">=</span><span class="n">clust</span><span class="o">.</span><span class="n">ordering_</span><span class="p">,</span>
<span class="n">eps</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">space</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">))</span>
<span class="n">reachability</span> <span class="o">=</span> <span class="n">clust</span><span class="o">.</span><span class="n">reachability_</span><span class="p">[</span><span class="n">clust</span><span class="o">.</span><span class="n">ordering_</span><span class="p">]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="n">clust</span><span class="o">.</span><span class="n">labels_</span><span class="p">[</span><span class="n">clust</span><span class="o">.</span><span class="n">ordering_</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">10</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<span class="n">G</span> <span class="o">=</span> <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.gridspec.GridSpec.html#matplotlib.gridspec.GridSpec" title="matplotlib.gridspec.GridSpec" class="sphx-glr-backref-module-matplotlib-gridspec sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">gridspec</span><span class="o">.</span><span class="n">GridSpec</span></a><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="n">ax1</span> <span class="o">=</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="n">G</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:])</span>
<span class="n">ax2</span> <span class="o">=</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="n">G</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="n">ax3</span> <span class="o">=</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="n">G</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="n">ax4</span> <span class="o">=</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="n">G</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="c1"># Reachability plot</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"g."</span><span class="p">,</span> <span class="s2">"r."</span><span class="p">,</span> <span class="s2">"b."</span><span class="p">,</span> <span class="s2">"y."</span><span class="p">,</span> <span class="s2">"c."</span><span class="p">]</span>
<span class="k">for</span> <span class="n">klass</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="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">Xk</span> <span class="o">=</span> <span class="n">space</span><span class="p">[</span><span class="n">labels</span> <span class="o">==</span> <span class="n">klass</span><span class="p">]</span>
<span class="n">Rk</span> <span class="o">=</span> <span class="n">reachability</span><span class="p">[</span><span class="n">labels</span> <span class="o">==</span> <span class="n">klass</span><span class="p">]</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Xk</span><span class="p">,</span> <span class="n">Rk</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">space</span><span class="p">[</span><span class="n">labels</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">reachability</span><span class="p">[</span><span class="n">labels</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="s2">"k."</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">space</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.full_like.html#numpy.full_like" title="numpy.full_like" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">full_like</span></a><span class="p">(</span><span class="n">space</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">),</span> <span class="s2">"k-"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">space</span><span class="p">,</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.full_like.html#numpy.full_like" title="numpy.full_like" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">full_like</span></a><span class="p">(</span><span class="n">space</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">),</span> <span class="s2">"k-."</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">"Reachability (epsilon distance)"</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Reachability Plot"</span><span class="p">)</span>
<span class="c1"># OPTICS</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"g."</span><span class="p">,</span> <span class="s2">"r."</span><span class="p">,</span> <span class="s2">"b."</span><span class="p">,</span> <span class="s2">"y."</span><span class="p">,</span> <span class="s2">"c."</span><span class="p">]</span>
<span class="k">for</span> <span class="n">klass</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="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">Xk</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">clust</span><span class="o">.</span><span class="n">labels_</span> <span class="o">==</span> <span class="n">klass</span><span class="p">]</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Xk</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Xk</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">clust</span><span class="o">.</span><span class="n">labels_</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</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">clust</span><span class="o">.</span><span class="n">labels_</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"k+"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Automatic Clustering</span><span class="se">\n</span><span class="s2">OPTICS"</span><span class="p">)</span>
<span class="c1"># DBSCAN at 0.5</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"g."</span><span class="p">,</span> <span class="s2">"r."</span><span class="p">,</span> <span class="s2">"b."</span><span class="p">,</span> <span class="s2">"c."</span><span class="p">]</span>
<span class="k">for</span> <span class="n">klass</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="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">Xk</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">labels_050</span> <span class="o">==</span> <span class="n">klass</span><span class="p">]</span>
<span class="n">ax3</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Xk</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Xk</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax3</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">labels_050</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</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">labels_050</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"k+"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">ax3</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Clustering at 0.5 epsilon cut</span><span class="se">\n</span><span class="s2">DBSCAN"</span><span class="p">)</span>
<span class="c1"># DBSCAN at 2.</span>
<span class="n">colors</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"g."</span><span class="p">,</span> <span class="s2">"m."</span><span class="p">,</span> <span class="s2">"y."</span><span class="p">,</span> <span class="s2">"c."</span><span class="p">]</span>
<span class="k">for</span> <span class="n">klass</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="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="n">colors</span><span class="p">):</span>
<span class="n">Xk</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">labels_200</span> <span class="o">==</span> <span class="n">klass</span><span class="p">]</span>
<span class="n">ax4</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">Xk</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">Xk</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="n">ax4</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">X</span><span class="p">[</span><span class="n">labels_200</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</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">labels_200</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"k+"</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
<span class="n">ax4</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Clustering at 2.0 epsilon cut</span><span class="se">\n</span><span class="s2">DBSCAN"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html#matplotlib.pyplot.tight_layout" title="matplotlib.pyplot.tight_layout" 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">tight_layout</span></a><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>
</pre></div>
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