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# Outlier detection with Local Outlier Factor (LOF)

The Local Outlier Factor (LOF) algorithm is an unsupervised anomaly detection method which computes the local density deviation of a given data point with respect to its neighbors. It considers as outliers the samples that have a substantially lower density than their neighbors. This example shows how to use LOF for outlier detection which is the default use case of this estimator in scikit-learn. Note that when LOF is used for outlier detection it has no `predict`, `decision_function` and `score_samples` methods. See the User Guide for details on the difference between outlier detection and novelty detection and how to use LOF for novelty detection.

The number of neighbors considered (parameter `n_neighbors`) is typically set 1) greater than the minimum number of samples a cluster has to contain, so that other samples can be local outliers relative to this cluster, and 2) smaller than the maximum number of close by samples that can potentially be local outliers. In practice, such information is generally not available, and taking `n_neighbors=20` appears to work well in general.

## Generate data with outliers

    import numpy as np

    np.random.seed(42)

    X_inliers = 0.3 * np.random.randn(100, 2)
    X_inliers = np.r_[X_inliers + 2, X_inliers - 2]
    X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))
    X = np.r_[X_inliers, X_outliers]

    n_outliers = len(X_outliers)
    ground_truth = np.ones(len(X), dtype=int)
    ground_truth[-n_outliers:] = -1

## Fit the model for outlier detection (default)

Use `fit_predict` to compute the predicted labels of the training samples (when LOF is used for outlier detection, the estimator has no `predict`, `decision_function` and `score_samples` methods).

    from sklearn.neighbors import LocalOutlierFactor

    clf = LocalOutlierFactor(n_neighbors=20, contamination=0.1)
    y_pred = clf.fit_predict(X)
    n_errors = (y_pred != ground_truth).sum()
    X_scores = clf.negative_outlier_factor_

## Plot results

    import matplotlib.pyplot as plt
    from matplotlib.legend_handler import HandlerPathCollection

    def update_legend_marker_size(handle, orig):
        "Customize size of the legend marker"
        handle.update_from(orig)
        handle.set_sizes([20])

    plt.scatter(X[:, 0], X[:, 1], color="k", s=3.0, label="Data points")
    # plot circles with radius proportional to the outlier scores
    radius = (X_scores.max() - X_scores) / (X_scores.max() - X_scores.min())
    scatter = plt.scatter(
        X[:, 0],
        X[:, 1],
        s=1000 * radius,
        edgecolors="r",
        facecolors="none",
        label="Outlier scores",
    )
    plt.axis("tight")
    plt.xlim((-5, 5))
    plt.ylim((-5, 5))
    plt.xlabel("prediction errors: %d" % (n_errors))
    plt.legend(
        handler_map={scatter: HandlerPathCollection(update_func=update_legend_marker_size)}
    )
    plt.title("Local Outlier Factor (LOF)")
    plt.show()

Total running time of the script: (0 minutes 0.056 seconds)

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