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<li><a class="reference internal" href="#">Outlier detection with several methods.</a></li>
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<div class="section" id="outlier-detection-with-several-methods">
<span id="sphx-glr-auto-examples-covariance-plot-outlier-detection-py"></span><h1>Outlier detection with several methods.<a class="headerlink" href="#outlier-detection-with-several-methods" title="Permalink to this headline">¶</a></h1>
<p>When the amount of contamination is known, this example illustrates three
different ways of performing <a class="reference internal" href="../../modules/outlier_detection.html#outlier-detection"><span class="std std-ref">Novelty and Outlier Detection</span></a>:</p>
<ul class="simple">
<li>based on a robust estimator of covariance, which is assuming that the
data are Gaussian distributed and performs better than the One-Class SVM
in that case.</li>
<li>using the One-Class SVM and its ability to capture the shape of the
data set, hence performing better when the data is strongly
non-Gaussian, i.e. with two well-separated clusters;</li>
<li>using the Isolation Forest algorithm, which is based on random forests and
hence more adapted to large-dimensional settings, even if it performs
quite well in the examples below.</li>
<li>using the Local Outlier Factor to measure the local deviation of a given
data point with respect to its neighbors by comparing their local density.</li>
</ul>
<p>The ground truth about inliers and outliers is given by the points colors
while the orange-filled area indicates which points are reported as inliers
by each method.</p>
<p>Here, we assume that we know the fraction of outliers in the datasets.
Thus rather than using the ‘predict’ method of the objects, we set the
threshold on the decision_function to separate out the corresponding
fraction.</p>
<ul class="sphx-glr-horizontal">
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_outlier_detection_001.png"><img alt="../../_images/sphx_glr_plot_outlier_detection_001.png" src="../../_images/sphx_glr_plot_outlier_detection_001.png" style="width: 423.0px; height: 329.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_outlier_detection_002.png"><img alt="../../_images/sphx_glr_plot_outlier_detection_002.png" src="../../_images/sphx_glr_plot_outlier_detection_002.png" style="width: 423.0px; height: 329.0px;" /></a>
</li>
<li><a class="first reference internal image-reference" href="../../_images/sphx_glr_plot_outlier_detection_003.png"><img alt="../../_images/sphx_glr_plot_outlier_detection_003.png" src="../../_images/sphx_glr_plot_outlier_detection_003.png" style="width: 423.0px; height: 329.0px;" /></a>
</li>
</ul>
<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">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</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">import</span> <span class="nn">matplotlib.font_manager</span>
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">svm</span>
<span class="kn">from</span> <span class="nn">sklearn.covariance</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="View documentation for sklearn.covariance.EllipticEnvelope"><span class="n">EllipticEnvelope</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="View documentation for sklearn.ensemble.IsolationForest"><span class="n">IsolationForest</span></a>
<span class="kn">from</span> <span class="nn">sklearn.neighbors</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="View documentation for sklearn.neighbors.LocalOutlierFactor"><span class="n">LocalOutlierFactor</span></a>
<span class="k">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>
<span class="n">rng</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.RandomState.wald.html#numpy.random.RandomState" title="View documentation for numpy.random.RandomState"><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="mi">42</span><span class="p">)</span>
<span class="c1"># Example settings</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">200</span>
<span class="n">outliers_fraction</span> <span class="o">=</span> <span class="mf">0.25</span>
<span class="n">clusters_separation</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</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"># define two outlier detection tools to be compared</span>
<span class="n">classifiers</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"One-Class SVM"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="View documentation for sklearn.svm.OneClassSVM"><span class="n">svm</span><span class="o">.</span><span class="n">OneClassSVM</span></a><span class="p">(</span><span class="n">nu</span><span class="o">=</span><span class="mf">0.95</span> <span class="o">*</span> <span class="n">outliers_fraction</span> <span class="o">+</span> <span class="mf">0.05</span><span class="p">,</span>
<span class="n">kernel</span><span class="o">=</span><span class="s2">"rbf"</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">0.1</span><span class="p">),</span>
<span class="s2">"Robust covariance"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="View documentation for sklearn.covariance.EllipticEnvelope"><span class="n">EllipticEnvelope</span></a><span class="p">(</span><span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">),</span>
<span class="s2">"Isolation Forest"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="View documentation for sklearn.ensemble.IsolationForest"><span class="n">IsolationForest</span></a><span class="p">(</span><span class="n">max_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span>
<span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">,</span>
<span class="n">random_state</span><span class="o">=</span><span class="n">rng</span><span class="p">),</span>
<span class="s2">"Local Outlier Factor"</span><span class="p">:</span> <a href="../../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="View documentation for sklearn.neighbors.LocalOutlierFactor"><span class="n">LocalOutlierFactor</span></a><span class="p">(</span>
<span class="n">n_neighbors</span><span class="o">=</span><span class="mi">35</span><span class="p">,</span>
<span class="n">contamination</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">)}</span>
<span class="c1"># Compare given classifiers under given settings</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</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><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="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">100</span><span class="p">),</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="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span>
<span class="n">n_inliers</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="mf">1.</span> <span class="o">-</span> <span class="n">outliers_fraction</span><span class="p">)</span> <span class="o">*</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">n_outliers</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">outliers_fraction</span> <span class="o">*</span> <span class="n">n_samples</span><span class="p">)</span>
<span class="n">ground_truth</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.ones.html#numpy.ones" title="View documentation for numpy.ones"><span class="n">np</span><span class="o">.</span><span class="n">ones</span></a><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
<span class="n">ground_truth</span><span class="p">[</span><span class="o">-</span><span class="n">n_outliers</span><span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="c1"># Fit the problem with varying cluster separation</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">offset</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">clusters_separation</span><span class="p">):</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">42</span><span class="p">)</span>
<span class="c1"># Data generation</span>
<span class="n">X1</span> <span class="o">=</span> <span class="mf">0.3</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_inliers</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="n">offset</span>
<span class="n">X2</span> <span class="o">=</span> <span class="mf">0.3</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_inliers</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">offset</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X1</span><span class="p">,</span> <span class="n">X2</span><span class="p">]</span>
<span class="c1"># Add outliers</span>
<span class="n">X</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.r_.html#numpy.r_" title="View documentation for numpy.r_"><span class="n">np</span><span class="o">.</span><span class="n">r_</span></a><span class="p">[</span><span class="n">X</span><span class="p">,</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.random.uniform.html#numpy.random.uniform" title="View documentation for numpy.random.uniform"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span></a><span class="p">(</span><span class="n">low</span><span class="o">=-</span><span class="mi">6</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">6</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">n_outliers</span><span class="p">,</span> <span class="mi">2</span><span class="p">))]</span>
<span class="c1"># Fit the model</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.figure.AxesStack.html#matplotlib.figure" title="View documentation for matplotlib.pyplot.figure"><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">9</span><span class="p">,</span> <span class="mi">7</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">clf_name</span><span class="p">,</span> <span class="n">clf</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">classifiers</span><span class="o">.</span><span class="n">items</span><span class="p">()):</span>
<span class="c1"># fit the data and tag outliers</span>
<span class="k">if</span> <span class="n">clf_name</span> <span class="o">==</span> <span class="s2">"Local Outlier Factor"</span><span class="p">:</span>
<span class="n">y_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">fit_predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">scores_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">negative_outlier_factor_</span>
<span class="k">else</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">scores_pred</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="n">y_pred</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="n">threshold</span> <span class="o">=</span> <span class="n">stats</span><span class="o">.</span><span class="n">scoreatpercentile</span><span class="p">(</span><span class="n">scores_pred</span><span class="p">,</span>
<span class="mi">100</span> <span class="o">*</span> <span class="n">outliers_fraction</span><span class="p">)</span>
<span class="n">n_errors</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_pred</span> <span class="o">!=</span> <span class="n">ground_truth</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="c1"># plot the levels lines and the points</span>
<span class="k">if</span> <span class="n">clf_name</span> <span class="o">==</span> <span class="s2">"Local Outlier Factor"</span><span class="p">:</span>
<span class="c1"># decision_function is private for LOF</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">_decision_function</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><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="k">else</span><span class="p">:</span>
<span class="n">Z</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><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="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">subplot</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><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="mi">2</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">subplot</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">levels</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="n">Z</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">threshold</span><span class="p">,</span> <span class="mi">7</span><span class="p">),</span>
<span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">Blues_r</span><span class="p">)</span>
<span class="n">a</span> <span class="o">=</span> <span class="n">subplot</span><span class="o">.</span><span class="n">contour</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">levels</span><span class="o">=</span><span class="p">[</span><span class="n">threshold</span><span class="p">],</span>
<span class="n">linewidths</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">colors</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span>
<span class="n">subplot</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">levels</span><span class="o">=</span><span class="p">[</span><span class="n">threshold</span><span class="p">,</span> <span class="n">Z</span><span class="o">.</span><span class="n">max</span><span class="p">()],</span>
<span class="n">colors</span><span class="o">=</span><span class="s1">'orange'</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">subplot</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="o">-</span><span class="n">n_outliers</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="o">-</span><span class="n">n_outliers</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="s1">'white'</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">subplot</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="o">-</span><span class="n">n_outliers</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="o">-</span><span class="n">n_outliers</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="s1">'black'</span><span class="p">,</span>
<span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">subplot</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'tight'</span><span class="p">)</span>
<span class="n">subplot</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span>
<span class="p">[</span><span class="n">a</span><span class="o">.</span><span class="n">collections</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">],</span>
<span class="p">[</span><span class="s1">'learned decision function'</span><span class="p">,</span> <span class="s1">'true inliers'</span><span class="p">,</span> <span class="s1">'true outliers'</span><span class="p">],</span>
<span class="n">prop</span><span class="o">=</span><span class="n">matplotlib</span><span class="o">.</span><span class="n">font_manager</span><span class="o">.</span><span class="n">FontProperties</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="mi">10</span><span class="p">),</span>
<span class="n">loc</span><span class="o">=</span><span class="s1">'lower right'</span><span class="p">)</span>
<span class="n">subplot</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">"</span><span class="si">%d</span><span class="s2">. </span><span class="si">%s</span><span class="s2"> (errors: </span><span class="si">%d</span><span class="s2">)"</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">clf_name</span><span class="p">,</span> <span class="n">n_errors</span><span class="p">))</span>
<span class="n">subplot</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">((</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<span class="n">subplot</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">((</span><span class="o">-</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="View documentation for matplotlib.pyplot.subplots_adjust"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="mf">0.04</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.96</span><span class="p">,</span> <span class="mf">0.94</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.26</span><span class="p">)</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="View documentation for matplotlib.pyplot.suptitle"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="s2">"Outlier detection"</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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