90 lines
3.5 KiB
Python
90 lines
3.5 KiB
Python
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"""
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=================================================
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Novelty detection with Local Outlier Factor (LOF)
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=================================================
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The Local Outlier Factor (LOF) algorithm is an unsupervised anomaly detection
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method which computes the local density deviation of a given data point with
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respect to its neighbors. It considers as outliers the samples that have a
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substantially lower density than their neighbors. This example shows how to
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use LOF for novelty detection. Note that when LOF is used for novelty
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detection you MUST not use predict, decision_function and score_samples on the
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training set as this would lead to wrong results. You must only use these
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methods on new unseen data (which are not in the training set). See
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:ref:`User Guide <outlier_detection>`: for details on the difference between
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outlier detection and novelty detection and how to use LOF for outlier
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detection.
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The number of neighbors considered, (parameter n_neighbors) is typically
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set 1) greater than the minimum number of samples a cluster has to contain,
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so that other samples can be local outliers relative to this cluster, and 2)
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smaller than the maximum number of close by samples that can potentially be
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local outliers.
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In practice, such information is generally not available, and taking
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n_neighbors=20 appears to work well in general.
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"""
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import matplotlib
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import matplotlib.lines as mlines
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.neighbors import LocalOutlierFactor
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np.random.seed(42)
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xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))
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# Generate normal (not abnormal) training observations
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X = 0.3 * np.random.randn(100, 2)
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X_train = np.r_[X + 2, X - 2]
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# Generate new normal (not abnormal) observations
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X = 0.3 * np.random.randn(20, 2)
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X_test = np.r_[X + 2, X - 2]
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# Generate some abnormal novel observations
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X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))
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# fit the model for novelty detection (novelty=True)
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clf = LocalOutlierFactor(n_neighbors=20, novelty=True, contamination=0.1)
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clf.fit(X_train)
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# DO NOT use predict, decision_function and score_samples on X_train as this
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# would give wrong results but only on new unseen data (not used in X_train),
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# e.g. X_test, X_outliers or the meshgrid
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y_pred_test = clf.predict(X_test)
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y_pred_outliers = clf.predict(X_outliers)
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n_error_test = y_pred_test[y_pred_test == -1].size
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n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size
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# plot the learned frontier, the points, and the nearest vectors to the plane
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Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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plt.title("Novelty Detection with LOF")
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plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu)
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a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors="darkred")
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plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors="palevioletred")
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s = 40
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b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k")
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b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k")
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c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k")
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plt.axis("tight")
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plt.xlim((-5, 5))
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plt.ylim((-5, 5))
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plt.legend(
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[mlines.Line2D([], [], color="darkred"), b1, b2, c],
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[
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"learned frontier",
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"training observations",
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"new regular observations",
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"new abnormal observations",
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],
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loc="upper left",
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prop=matplotlib.font_manager.FontProperties(size=11),
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)
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plt.xlabel(
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"errors novel regular: %d/40 ; errors novel abnormal: %d/40"
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% (n_error_test, n_error_outliers)
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)
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plt.show()
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