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<li><a class="reference internal" href="#">Comparing anomaly detection algorithms for outlier detection on toy datasets</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-miscellaneous-plot-anomaly-comparison-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="comparing-anomaly-detection-algorithms-for-outlier-detection-on-toy-datasets">
<span id="sphx-glr-auto-examples-miscellaneous-plot-anomaly-comparison-py"></span><h1>Comparing anomaly detection algorithms for outlier detection on toy datasets<a class="headerlink" href="#comparing-anomaly-detection-algorithms-for-outlier-detection-on-toy-datasets" title="Link to this heading">¶</a></h1>
<p>This example shows characteristics of different anomaly detection algorithms
on 2D datasets. Datasets contain one or two modes (regions of high density)
to illustrate the ability of algorithms to cope with multimodal data.</p>
<p>For each dataset, 15% of samples are generated as random uniform noise. This
proportion is the value given to the nu parameter of the OneClassSVM and the
contamination parameter of the other outlier detection algorithms.
Decision boundaries between inliers and outliers are displayed in black
except for Local Outlier Factor (LOF) as it has no predict method to be applied
on new data when it is used for outlier detection.</p>
<p>The <a class="reference internal" href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">OneClassSVM</span></code></a> is known to be sensitive to outliers and
thus does not perform very well for outlier detection. This estimator is best
suited for novelty detection when the training set is not contaminated by
outliers. That said, outlier detection in high-dimension, or without any
assumptions on the distribution of the inlying data is very challenging, and a
One-class SVM might give useful results in these situations depending on the
value of its hyperparameters.</p>
<p>The <a class="reference internal" href="../../modules/generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.linear_model.SGDOneClassSVM</span></code></a> is an implementation of the
One-Class SVM based on stochastic gradient descent (SGD). Combined with kernel
approximation, this estimator can be used to approximate the solution
of a kernelized <a class="reference internal" href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.svm.OneClassSVM</span></code></a>. We note that, although not
identical, the decision boundaries of the
<a class="reference internal" href="../../modules/generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.linear_model.SGDOneClassSVM</span></code></a> and the ones of
<a class="reference internal" href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.svm.OneClassSVM</span></code></a> are very similar. The main advantage of using
<a class="reference internal" href="../../modules/generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.linear_model.SGDOneClassSVM</span></code></a> is that it scales linearly with
the number of samples.</p>
<p><a class="reference internal" href="../../modules/generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope"><code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.covariance.EllipticEnvelope</span></code></a> assumes the data is Gaussian and
learns an ellipse. It thus degrades when the data is not unimodal. Notice
however that this estimator is robust to outliers.</p>
<p><a class="reference internal" href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest"><code class="xref py py-class docutils literal notranslate"><span class="pre">IsolationForest</span></code></a> and
<a class="reference internal" href="../../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">LocalOutlierFactor</span></code></a> seem to perform reasonably well
for multi-modal data sets. The advantage of
<a class="reference internal" href="../../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor"><code class="xref py py-class docutils literal notranslate"><span class="pre">LocalOutlierFactor</span></code></a> over the other estimators is
shown for the third data set, where the two modes have different densities.
This advantage is explained by the local aspect of LOF, meaning that it only
compares the score of abnormality of one sample with the scores of its
neighbors.</p>
<p>Finally, for the last data set, it is hard to say that one sample is more
abnormal than another sample as they are uniformly distributed in a
hypercube. Except for the <a class="reference internal" href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM"><code class="xref py py-class docutils literal notranslate"><span class="pre">OneClassSVM</span></code></a> which overfits a
little, all estimators present decent solutions for this situation. In such a
case, it would be wise to look more closely at the scores of abnormality of
the samples as a good estimator should assign similar scores to all the
samples.</p>
<p>While these examples give some intuition about the algorithms, this
intuition might not apply to very high dimensional data.</p>
<p>Finally, note that parameters of the models have been here handpicked but
that in practice they need to be adjusted. In the absence of labelled data,
the problem is completely unsupervised so model selection can be a challenge.</p>
<img src="../../_images/sphx_glr_plot_anomaly_comparison_001.png" srcset="../../_images/sphx_glr_plot_anomaly_comparison_001.png" alt="Robust covariance, One-Class SVM, One-Class SVM (SGD), Isolation Forest, Local Outlier Factor" class = "sphx-glr-single-img"/><div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Alexandre Gramfort &lt;alexandre.gramfort@inria.fr&gt;</span>
<span class="c1">#         Albert Thomas &lt;albert.thomas@telecom-paristech.fr&gt;</span>
<span class="c1"># License: BSD 3 clause</span>

<span class="kn">import</span> <span class="nn">time</span>

<span class="kn">import</span> <span class="nn">matplotlib</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</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="sklearn.covariance.EllipticEnvelope" class="sphx-glr-backref-module-sklearn-covariance sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">EllipticEnvelope</span></a>
<span class="kn">from</span> <span class="nn">sklearn.datasets</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="p">,</span> <a href="../../modules/generated/sklearn.datasets.make_moons.html#sklearn.datasets.make_moons" title="sklearn.datasets.make_moons" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_moons</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="sklearn.ensemble.IsolationForest" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">IsolationForest</span></a>
<span class="kn">from</span> <span class="nn">sklearn.kernel_approximation</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.kernel_approximation.Nystroem.html#sklearn.kernel_approximation.Nystroem" title="sklearn.kernel_approximation.Nystroem" class="sphx-glr-backref-module-sklearn-kernel_approximation sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Nystroem</span></a>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SGDOneClassSVM</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="sklearn.neighbors.LocalOutlierFactor" class="sphx-glr-backref-module-sklearn-neighbors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">LocalOutlierFactor</span></a>
<span class="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a>

<a href="https://matplotlib.org/stable/api/matplotlib_configuration_api.html#matplotlib.rcParams" title="matplotlib.rcParams" class="sphx-glr-backref-module-matplotlib sphx-glr-backref-type-py-data"><span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span></a><span class="p">[</span><span class="s2">&quot;contour.negative_linestyle&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;solid&quot;</span>

<span class="c1"># Example settings</span>
<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">300</span>
<span class="n">outliers_fraction</span> <span class="o">=</span> <span class="mf">0.15</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">n_inliers</span> <span class="o">=</span> <span class="n">n_samples</span> <span class="o">-</span> <span class="n">n_outliers</span>

<span class="c1"># define outlier/anomaly detection methods to be compared.</span>
<span class="c1"># the SGDOneClassSVM must be used in a pipeline with a kernel approximation</span>
<span class="c1"># to give similar results to the OneClassSVM</span>
<span class="n">anomaly_algorithms</span> <span class="o">=</span> <span class="p">[</span>
    <span class="p">(</span>
        <span class="s2">&quot;Robust covariance&quot;</span><span class="p">,</span>
        <a href="../../modules/generated/sklearn.covariance.EllipticEnvelope.html#sklearn.covariance.EllipticEnvelope" title="sklearn.covariance.EllipticEnvelope" class="sphx-glr-backref-module-sklearn-covariance sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">),</span>
    <span class="p">),</span>
    <span class="p">(</span><span class="s2">&quot;One-Class SVM&quot;</span><span class="p">,</span> <a href="../../modules/generated/sklearn.svm.OneClassSVM.html#sklearn.svm.OneClassSVM" title="sklearn.svm.OneClassSVM" class="sphx-glr-backref-module-sklearn-svm sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="n">outliers_fraction</span><span class="p">,</span> <span class="n">kernel</span><span class="o">=</span><span class="s2">&quot;rbf&quot;</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="p">(</span>
        <span class="s2">&quot;One-Class SVM (SGD)&quot;</span><span class="p">,</span>
        <a href="../../modules/generated/sklearn.pipeline.make_pipeline.html#sklearn.pipeline.make_pipeline" title="sklearn.pipeline.make_pipeline" class="sphx-glr-backref-module-sklearn-pipeline sphx-glr-backref-type-py-function"><span class="n">make_pipeline</span></a><span class="p">(</span>
            <a href="../../modules/generated/sklearn.kernel_approximation.Nystroem.html#sklearn.kernel_approximation.Nystroem" title="sklearn.kernel_approximation.Nystroem" class="sphx-glr-backref-module-sklearn-kernel_approximation sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">Nystroem</span></a><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="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span> <span class="n">n_components</span><span class="o">=</span><span class="mi">150</span><span class="p">),</span>
            <a href="../../modules/generated/sklearn.linear_model.SGDOneClassSVM.html#sklearn.linear_model.SGDOneClassSVM" title="sklearn.linear_model.SGDOneClassSVM" class="sphx-glr-backref-module-sklearn-linear_model sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">SGDOneClassSVM</span></a><span class="p">(</span>
                <span class="n">nu</span><span class="o">=</span><span class="n">outliers_fraction</span><span class="p">,</span>
                <span class="n">shuffle</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
                <span class="n">fit_intercept</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
                <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">,</span>
                <span class="n">tol</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span>
            <span class="p">),</span>
        <span class="p">),</span>
    <span class="p">),</span>
    <span class="p">(</span>
        <span class="s2">&quot;Isolation Forest&quot;</span><span class="p">,</span>
        <a href="../../modules/generated/sklearn.ensemble.IsolationForest.html#sklearn.ensemble.IsolationForest" title="sklearn.ensemble.IsolationForest" class="sphx-glr-backref-module-sklearn-ensemble sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">IsolationForest</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="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">),</span>
    <span class="p">),</span>
    <span class="p">(</span>
        <span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">,</span>
        <a href="../../modules/generated/sklearn.neighbors.LocalOutlierFactor.html#sklearn.neighbors.LocalOutlierFactor" title="sklearn.neighbors.LocalOutlierFactor" class="sphx-glr-backref-module-sklearn-neighbors sphx-glr-backref-type-py-class sphx-glr-backref-instance"><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="p">),</span>
<span class="p">]</span>

<span class="c1"># Define datasets</span>
<span class="n">blobs_params</span> <span class="o">=</span> <span class="nb">dict</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">n_samples</span><span class="o">=</span><span class="n">n_inliers</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">datasets</span> <span class="o">=</span> <span class="p">[</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">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</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">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</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">centers</span><span class="o">=</span><span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]],</span> <span class="n">cluster_std</span><span class="o">=</span><span class="p">[</span><span class="mf">1.5</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">],</span> <span class="o">**</span><span class="n">blobs_params</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span>
    <span class="mf">4.0</span>
    <span class="o">*</span> <span class="p">(</span>
        <a href="../../modules/generated/sklearn.datasets.make_moons.html#sklearn.datasets.make_moons" title="sklearn.datasets.make_moons" class="sphx-glr-backref-module-sklearn-datasets sphx-glr-backref-type-py-function"><span class="n">make_moons</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.05</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="mi">0</span><span class="p">]</span>
        <span class="o">-</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">])</span>
    <span class="p">),</span>
    <span class="mf">14.0</span> <span class="o">*</span> <span class="p">(</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="mi">42</span><span class="p">)</span><span class="o">.</span><span class="n">rand</span><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> <span class="mf">0.5</span><span class="p">),</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="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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">150</span><span class="p">),</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><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">150</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="nb">len</span><span class="p">(</span><span class="n">anomaly_algorithms</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span><span class="p">,</span> <span class="mf">12.5</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">left</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span> <span class="n">right</span><span class="o">=</span><span class="mf">0.98</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="mf">0.96</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">hspace</span><span class="o">=</span><span class="mf">0.01</span>
<span class="p">)</span>

<span class="n">plot_num</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">rng</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="mi">42</span><span class="p">)</span>

<span class="k">for</span> <span class="n">i_dataset</span><span class="p">,</span> <span class="n">X</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">datasets</span><span class="p">):</span>
    <span class="c1"># Add outliers</span>
    <span class="n">X</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html#numpy.concatenate" title="numpy.concatenate" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">([</span><span class="n">X</span><span class="p">,</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><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="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>

    <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">algorithm</span> <span class="ow">in</span> <span class="n">anomaly_algorithms</span><span class="p">:</span>
        <span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
        <span class="n">algorithm</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">t1</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span><span class="o">.</span><span class="n">time</span></a><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="nb">len</span><span class="p">(</span><span class="n">datasets</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">anomaly_algorithms</span><span class="p">),</span> <span class="n">plot_num</span><span class="p">)</span>
        <span class="k">if</span> <span class="n">i_dataset</span> <span class="o">==</span> <span class="mi">0</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="n">name</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">18</span><span class="p">)</span>

        <span class="c1"># fit the data and tag outliers</span>
        <span class="k">if</span> <span class="n">name</span> <span class="o">==</span> <span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">:</span>
            <span class="n">y_pred</span> <span class="o">=</span> <span class="n">algorithm</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="k">else</span><span class="p">:</span>
            <span class="n">y_pred</span> <span class="o">=</span> <span class="n">algorithm</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="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>

        <span class="c1"># plot the levels lines and the points</span>
        <span class="k">if</span> <span class="n">name</span> <span class="o">!=</span> <span class="s2">&quot;Local Outlier Factor&quot;</span><span class="p">:</span>  <span class="c1"># LOF does not implement predict</span>
            <span class="n">Z</span> <span class="o">=</span> <span class="n">algorithm</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.c_.html#numpy.c_" title="numpy.c_" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><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>
            <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contour.html#matplotlib.pyplot.contour" title="matplotlib.pyplot.contour" 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">contour</span></a><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="mi">0</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="s2">&quot;black&quot;</span><span class="p">)</span>

        <span class="n">colors</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="s2">&quot;#377eb8&quot;</span><span class="p">,</span> <span class="s2">&quot;#ff7f00&quot;</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">X</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="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">colors</span><span class="p">[(</span><span class="n">y_pred</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">])</span>

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        <a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylim.html#matplotlib.pyplot.ylim" title="matplotlib.pyplot.ylim" 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">ylim</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>
        <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>
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            <span class="p">(</span><span class="s2">&quot;</span><span class="si">%.2f</span><span class="s2">s&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">t1</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span><span class="o">.</span><span class="n">lstrip</span><span class="p">(</span><span class="s2">&quot;0&quot;</span><span class="p">),</span>
            <span class="n">transform</span><span class="o">=</span><a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.gca.html#matplotlib.pyplot.gca" title="matplotlib.pyplot.gca" 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">gca</span></a><span class="p">()</span><span class="o">.</span><span class="n">transAxes</span><span class="p">,</span>
            <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span>
            <span class="n">horizontalalignment</span><span class="o">=</span><span class="s2">&quot;right&quot;</span><span class="p">,</span>
        <span class="p">)</span>
        <span class="n">plot_num</span> <span class="o">+=</span> <span class="mi">1</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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