124 lines
4.2 KiB
Python
124 lines
4.2 KiB
Python
"""
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=======================
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IsolationForest example
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=======================
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An example using :class:`~sklearn.ensemble.IsolationForest` for anomaly
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detection.
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The :ref:`isolation_forest` is an ensemble of "Isolation Trees" that "isolate"
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observations by recursive random partitioning, which can be represented by a
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tree structure. The number of splittings required to isolate a sample is lower
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for outliers and higher for inliers.
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In the present example we demo two ways to visualize the decision boundary of an
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Isolation Forest trained on a toy dataset.
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"""
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# %%
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# Data generation
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# ---------------
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#
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# We generate two clusters (each one containing `n_samples`) by randomly
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# sampling the standard normal distribution as returned by
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# :func:`numpy.random.randn`. One of them is spherical and the other one is
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# slightly deformed.
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#
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# For consistency with the :class:`~sklearn.ensemble.IsolationForest` notation,
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# the inliers (i.e. the gaussian clusters) are assigned a ground truth label `1`
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# whereas the outliers (created with :func:`numpy.random.uniform`) are assigned
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# the label `-1`.
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import numpy as np
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from sklearn.model_selection import train_test_split
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n_samples, n_outliers = 120, 40
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rng = np.random.RandomState(0)
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covariance = np.array([[0.5, -0.1], [0.7, 0.4]])
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cluster_1 = 0.4 * rng.randn(n_samples, 2) @ covariance + np.array([2, 2]) # general
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cluster_2 = 0.3 * rng.randn(n_samples, 2) + np.array([-2, -2]) # spherical
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outliers = rng.uniform(low=-4, high=4, size=(n_outliers, 2))
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X = np.concatenate([cluster_1, cluster_2, outliers])
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y = np.concatenate(
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[np.ones((2 * n_samples), dtype=int), -np.ones((n_outliers), dtype=int)]
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)
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X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y, random_state=42)
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# %%
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# We can visualize the resulting clusters:
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import matplotlib.pyplot as plt
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scatter = plt.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
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handles, labels = scatter.legend_elements()
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plt.axis("square")
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plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
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plt.title("Gaussian inliers with \nuniformly distributed outliers")
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plt.show()
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# %%
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# Training of the model
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# ---------------------
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from sklearn.ensemble import IsolationForest
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clf = IsolationForest(max_samples=100, random_state=0)
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clf.fit(X_train)
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# %%
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# Plot discrete decision boundary
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# -------------------------------
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#
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# We use the class :class:`~sklearn.inspection.DecisionBoundaryDisplay` to
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# visualize a discrete decision boundary. The background color represents
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# whether a sample in that given area is predicted to be an outlier
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# or not. The scatter plot displays the true labels.
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import matplotlib.pyplot as plt
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from sklearn.inspection import DecisionBoundaryDisplay
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disp = DecisionBoundaryDisplay.from_estimator(
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clf,
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X,
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response_method="predict",
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alpha=0.5,
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)
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disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
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disp.ax_.set_title("Binary decision boundary \nof IsolationForest")
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plt.axis("square")
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plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
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plt.show()
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# %%
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# Plot path length decision boundary
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# ----------------------------------
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#
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# By setting the `response_method="decision_function"`, the background of the
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# :class:`~sklearn.inspection.DecisionBoundaryDisplay` represents the measure of
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# normality of an observation. Such score is given by the path length averaged
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# over a forest of random trees, which itself is given by the depth of the leaf
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# (or equivalently the number of splits) required to isolate a given sample.
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#
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# When a forest of random trees collectively produce short path lengths for
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# isolating some particular samples, they are highly likely to be anomalies and
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# the measure of normality is close to `0`. Similarly, large paths correspond to
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# values close to `1` and are more likely to be inliers.
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disp = DecisionBoundaryDisplay.from_estimator(
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clf,
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X,
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response_method="decision_function",
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alpha=0.5,
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)
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disp.ax_.scatter(X[:, 0], X[:, 1], c=y, s=20, edgecolor="k")
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disp.ax_.set_title("Path length decision boundary \nof IsolationForest")
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plt.axis("square")
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plt.legend(handles=handles, labels=["outliers", "inliers"], title="true class")
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plt.colorbar(disp.ax_.collections[1])
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plt.show()
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