
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/ensemble/plot_isolation_forest.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_ensemble_plot_isolation_forest.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_ensemble_plot_isolation_forest.py:


=======================
IsolationForest example
=======================

An example using :class:`~sklearn.ensemble.IsolationForest` for anomaly
detection.

The :ref:`isolation_forest` is an ensemble of "Isolation Trees" that "isolate"
observations by recursive random partitioning, which can be represented by a
tree structure. The number of splittings required to isolate a sample is lower
for outliers and higher for inliers.

In the present example we demo two ways to visualize the decision boundary of an
Isolation Forest trained on a toy dataset.

.. GENERATED FROM PYTHON SOURCE LINES 18-22

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 23-35

Data generation
---------------

We generate two clusters (each one containing `n_samples`) by randomly
sampling the standard normal distribution as returned by
:func:`numpy.random.randn`. One of them is spherical and the other one is
slightly deformed.

For consistency with the :class:`~sklearn.ensemble.IsolationForest` notation,
the inliers (i.e. the gaussian clusters) are assigned a ground truth label `1`
whereas the outliers (created with :func:`numpy.random.uniform`) are assigned
the label `-1`.

.. GENERATED FROM PYTHON SOURCE LINES 35-54

.. code-block:: Python


    import numpy as np

    from sklearn.model_selection import train_test_split

    n_samples, n_outliers = 120, 40
    rng = np.random.RandomState(0)
    covariance = np.array([[0.5, -0.1], [0.7, 0.4]])
    cluster_1 = 0.4 * rng.randn(n_samples, 2) @ covariance + np.array([2, 2])  # general
    cluster_2 = 0.3 * rng.randn(n_samples, 2) + np.array([-2, -2])  # spherical
    outliers = rng.uniform(low=-4, high=4, size=(n_outliers, 2))

    X = np.concatenate([cluster_1, cluster_2, outliers])
    y = np.concatenate(
        [np.ones((2 * n_samples), dtype=int), -np.ones((n_outliers), dtype=int)]
    )

    X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)








.. GENERATED FROM PYTHON SOURCE LINES 55-56

We can visualize the resulting clusters:

.. GENERATED FROM PYTHON SOURCE LINES 56-66

.. code-block:: Python


    import matplotlib.pyplot as plt

    scatter = plt.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
    handles, labels = scatter.legend_elements()
    plt.axis("square")
    plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
    plt.title("Gaussian inliers with \nuniformly distributed outliers")
    plt.show()




.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_001.png
   :alt: Gaussian inliers with  uniformly distributed outliers
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 67-69

Training of the model
---------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-75

.. code-block:: Python


    from sklearn.ensemble import IsolationForest

    clf = IsolationForest(max_samples=100, random_state=0)
    clf.fit(X_train)






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      width: 100%;
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    </style><body><div id="sk-container-id-17" tabindex="0" class="sk-top-container sk-global"><div class="sk-text-repr-fallback"><pre>IsolationForest(max_samples=100, random_state=0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually sk-global" id="sk-estimator-id-51" type="checkbox" checked><label for="sk-estimator-id-51" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>IsolationForest</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html">?<span>Documentation for IsolationForest</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" data-param-prefix="">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_samples',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-max_samples;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=max_samples,-%22auto%22%2C%20int%20or%20float%2C%20default%3D%22auto%22">
                max_samples
                <span class="param-doc-description"
                style="position-anchor: --doc-link-max_samples;">
                max_samples: &quot;auto&quot;, int or float, default=&quot;auto&quot;<br><br>The number of samples to draw from X to train each base estimator.<br><br>- If int, then draw `max_samples` samples.<br>- If float, then draw `max_samples * X.shape[0]` samples.<br>- If &quot;auto&quot;, then `max_samples=min(256, n_samples)`.<br><br>If max_samples is larger than the number of samples provided,<br>all samples will be used for all trees (no sampling).</span>
            </a>
        </td>
                <td class="value">100</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('random_state',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-random_state;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=random_state,-int%2C%20RandomState%20instance%20or%20None%2C%20default%3DNone">
                random_state
                <span class="param-doc-description"
                style="position-anchor: --doc-link-random_state;">
                random_state: int, RandomState instance or None, default=None<br><br>Controls the pseudo-randomness of the selection of the feature<br>and split values for each branching step and each tree in the forest.<br><br>Pass an int for reproducible results across multiple function calls.<br>See :term:`Glossary &lt;random_state&gt;`.</span>
            </a>
        </td>
                <td class="value">0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_estimators',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_estimators;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=n_estimators,-int%2C%20default%3D100">
                n_estimators
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_estimators;">
                n_estimators: int, default=100<br><br>The number of base estimators in the ensemble.</span>
            </a>
        </td>
                <td class="value">100</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('contamination',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-contamination;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=contamination,-%27auto%27%20or%20float%2C%20default%3D%27auto%27">
                contamination
                <span class="param-doc-description"
                style="position-anchor: --doc-link-contamination;">
                contamination: &#x27;auto&#x27; or float, default=&#x27;auto&#x27;<br><br>The amount of contamination of the data set, i.e. the proportion<br>of outliers in the data set. Used when fitting to define the threshold<br>on the scores of the samples.<br><br>- If &#x27;auto&#x27;, the threshold is determined as in the<br>  original paper.<br>- If float, the contamination should be in the range (0, 0.5].<br><br>.. versionchanged:: 0.22<br>   The default value of ``contamination`` changed from 0.1<br>   to ``&#x27;auto&#x27;``.</span>
            </a>
        </td>
                <td class="value">&#x27;auto&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_features',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-max_features;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=max_features,-int%20or%20float%2C%20default%3D1.0">
                max_features
                <span class="param-doc-description"
                style="position-anchor: --doc-link-max_features;">
                max_features: int or float, default=1.0<br><br>The number of features to draw from X to train each base estimator.<br><br>- If int, then draw `max_features` features.<br>- If float, then draw `max(1, int(max_features * n_features_in_))` features.<br><br>Note: using a float number less than 1.0 or integer less than number of<br>features will enable feature subsampling and leads to a longer runtime.</span>
            </a>
        </td>
                <td class="value">1.0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('bootstrap',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-bootstrap;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=bootstrap,-bool%2C%20default%3DFalse">
                bootstrap
                <span class="param-doc-description"
                style="position-anchor: --doc-link-bootstrap;">
                bootstrap: bool, default=False<br><br>If True, individual trees are fit on random subsets of the training<br>data sampled with replacement. If False, sampling without replacement<br>is performed.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_jobs',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_jobs;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=n_jobs,-int%2C%20default%3DNone">
                n_jobs
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_jobs;">
                n_jobs: int, default=None<br><br>The number of jobs to run in parallel for :meth:`fit`. ``None`` means 1<br>unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using<br>all processors. See :term:`Glossary &lt;n_jobs&gt;` for more details.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('verbose',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-verbose;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=verbose,-int%2C%20default%3D0">
                verbose
                <span class="param-doc-description"
                style="position-anchor: --doc-link-verbose;">
                verbose: int, default=0<br><br>Controls the verbosity of the tree building process.</span>
            </a>
        </td>
                <td class="value">0</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('warm_start',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-warm_start;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=warm_start,-bool%2C%20default%3DFalse">
                warm_start
                <span class="param-doc-description"
                style="position-anchor: --doc-link-warm_start;">
                warm_start: bool, default=False<br><br>When set to ``True``, reuse the solution of the previous call to fit<br>and add more estimators to the ensemble, otherwise, just fit a whole<br>new forest. See :term:`the Glossary &lt;warm_start&gt;`.<br><br>.. versionadded:: 0.21</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
    
            <div class="estimator-table">
                <details>
                    <summary>Fitted attributes</summary>
                    <table class="parameters-table">
                        <tbody>
                            <tr>
                            <th>Name</th>
                            <th>Type</th>
                            <th>Value</th>
                            </tr>
                        
           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-estimator_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=estimator_,-%3Aclass%3A~sklearn.tree.ExtraTreeRegressor%20instance">
                estimator_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-estimator_;">
                estimator_: :class:`~sklearn.tree.ExtraTreeRegressor` instance<br><br>The child estimator template used to create the collection of<br>fitted sub-estimators.<br><br>.. versionadded:: 1.2<br>   `base_estimator_` was renamed to `estimator_`.</span>
            </a>
        </td>
               <td class="fitted-att-type">ExtraTreeRegressor</td>
               <td>ExtraTreeRegr...andom_state=0)</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-estimators_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=estimators_,-list%20of%20ExtraTreeRegressor%20instances">
                estimators_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-estimators_;">
                estimators_: list of ExtraTreeRegressor instances<br><br>The collection of fitted sub-estimators.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[ExtraTreeRegr...te=2087557356), ExtraTreeRegr...ate=132990059), ExtraTreeRegr...te=1109697837), ExtraTreeRegr...ate=123230084), ...]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-estimators_features_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=estimators_features_,-list%20of%20ndarray">
                estimators_features_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-estimators_features_;">
                estimators_features_: list of ndarray<br><br>The subset of drawn features for each base estimator.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[array([0, 1]), array([0, 1]), array([0, 1]), array([0, 1]), ...]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-estimators_samples_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=estimators_samples_,-list%20of%20ndarray">
                estimators_samples_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-estimators_samples_;">
                estimators_samples_: list of ndarray<br><br>The subset of drawn samples (i.e., the in-bag samples) for each base<br>estimator.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[array([131,  ...57,  12,  61]), array([  3, 1...36, 124,  16]), array([146,  ...16, 124,  78]), array([183, 1...99,  61,  78]), ...]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-max_samples_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=max_samples_,-int">
                max_samples_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-max_samples_;">
                max_samples_: int<br><br>The actual number of samples.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>100</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_features_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=n_features_in_,-int">
                n_features_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_features_in_;">
                n_features_in_: int<br><br>Number of features seen during :term:`fit`.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>2</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-offset_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.ensemble.IsolationForest.html#:~:text=offset_,-float">
                offset_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-offset_;">
                offset_: float<br><br>Offset used to define the decision function from the raw scores. We<br>have the relation: ``decision_function = score_samples - offset_``.<br>``offset_`` is defined as follows. When the contamination parameter is<br>set to &quot;auto&quot;, the offset is equal to -0.5 as the scores of inliers are<br>close to 0 and the scores of outliers are close to -1. When a<br>contamination parameter different than &quot;auto&quot; is provided, the offset<br>is defined in such a way we obtain the expected number of outliers<br>(samples with decision function &lt; 0) in training.<br><br>.. versionadded:: 0.20</span>
            </a>
        </td>
               <td class="fitted-att-type">float</td>
               <td>-0.5</td>


           </tr>
    
                        </tbody>
                    </table>
                </details>
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.. GENERATED FROM PYTHON SOURCE LINES 76-83

Plot discrete decision boundary
-------------------------------

We use the class :class:`~sklearn.inspection.DecisionBoundaryDisplay` to
visualize a discrete decision boundary. The background color represents
whether a sample in that given area is predicted to be an outlier
or not. The scatter plot displays the true labels.

.. GENERATED FROM PYTHON SOURCE LINES 83-100

.. code-block:: Python


    import matplotlib.pyplot as plt

    from sklearn.inspection import DecisionBoundaryDisplay

    disp = DecisionBoundaryDisplay.from_estimator(
        clf,
        X,
        response_method="predict",
        alpha=0.5,
    )
    disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
    disp.ax_.set_title("Binary decision boundary \nof IsolationForest")
    plt.axis("square")
    plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
    plt.show()




.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_002.png
   :alt: Binary decision boundary  of IsolationForest
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 101-114

Plot path length decision boundary
----------------------------------

By setting the `response_method="decision_function"`, the background of the
:class:`~sklearn.inspection.DecisionBoundaryDisplay` represents the measure of
normality of an observation. Such score is given by the path length averaged
over a forest of random trees, which itself is given by the depth of the leaf
(or equivalently the number of splits) required to isolate a given sample.

When a forest of random trees collectively produce short path lengths for
isolating some particular samples, they are highly likely to be anomalies and
the measure of normality is close to `0`. Similarly, large paths correspond to
values close to `1` and are more likely to be inliers.

.. GENERATED FROM PYTHON SOURCE LINES 114-127

.. code-block:: Python


    disp = DecisionBoundaryDisplay.from_estimator(
        clf,
        X,
        response_method="decision_function",
        alpha=0.5,
    )
    disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
    disp.ax_.set_title("Path length decision boundary \nof IsolationForest")
    plt.axis("square")
    plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
    plt.colorbar(disp.ax_.collections[1])
    plt.show()



.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_003.png
   :alt: Path length decision boundary  of IsolationForest
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_isolation_forest_003.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.454 seconds)


.. _sphx_glr_download_auto_examples_ensemble_plot_isolation_forest.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_isolation_forest.ipynb <plot_isolation_forest.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_isolation_forest.py <plot_isolation_forest.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_isolation_forest.zip <plot_isolation_forest.zip>`


.. include:: plot_isolation_forest.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
