.. 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 ` to download the full example code or to run this example in your browser via JupyterLite or Binder .. 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 20-32 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 32-51 .. 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 52-53 We can visualize the resulting clusters: .. GENERATED FROM PYTHON SOURCE LINES 53-63 .. 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 64-66 Training of the model --------------------- .. GENERATED FROM PYTHON SOURCE LINES 66-72 .. code-block:: Python from sklearn.ensemble import IsolationForest clf = IsolationForest(max_samples=100, random_state=0) clf.fit(X_train) .. raw:: html

IsolationForest(max_samples=100, random_state=0)

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.. GENERATED FROM PYTHON SOURCE LINES 73-80 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 80-97 .. 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 98-111 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 111-124 .. 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 0.445 seconds) .. _sphx_glr_download_auto_examples_ensemble_plot_isolation_forest.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/ensemble/plot_isolation_forest.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/ensemble/plot_isolation_forest.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_isolation_forest.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_isolation_forest.py ` .. include:: plot_isolation_forest.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_