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Plot Lof Novelty Detection

================================================= Novelty 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 novelty detection. Note that when LOF is used for novelty detection you MUST not use predict, decision_function and score_samples on the training set as this would lead to wrong results. You must only use these methods on new unseen data (which are not in the training set). See

ref:

User Guide <outlier_detection>: for details on the difference between outlier detection and novelty detection and how to use LOF for outlier 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.

Imports for Novelty Detection with Local Outlier Factor

LOF for novelty detection requires the novelty=True flag: LocalOutlierFactor with novelty=True learns a density-based model of the training data and exposes predict, decision_function, and score_samples methods for scoring new, unseen data points. The LOF score for a point measures how much its local density (estimated from its k nearest neighbors) deviates from the local densities of those neighbors – a score significantly less than 1 indicates the point lies in a sparser region than its neighbors, flagging it as anomalous. The contamination=0.1 parameter sets the decision threshold by assuming 10% of data may be outliers, which determines the boundary contour separating inliers (label +1) from outliers (label -1).

Critical distinction between novelty detection and outlier detection: In novelty detection mode, the model must be fitted on clean (inlier-only) training data, and predict/decision_function must only be called on new test data – calling these on the training set would produce incorrect results because LOF’s local density comparisons assume training points are the reference distribution. The meshgrid-based decision_function evaluation generates the smooth decision boundary contour, while X_test (new normal observations) and X_outliers (anomalous observations) are scored separately. The n_neighbors=20 parameter balances sensitivity: too few neighbors makes LOF unstable to local noise, while too many averages out genuine local density variations that distinguish boundary inliers from true outliers.

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

import matplotlib
import matplotlib.lines as mlines
import matplotlib.pyplot as plt
import numpy as np

from sklearn.neighbors import LocalOutlierFactor

np.random.seed(42)

xx, yy = np.meshgrid(np.linspace(-5, 5, 500), np.linspace(-5, 5, 500))
# Generate normal (not abnormal) training observations
X = 0.3 * np.random.randn(100, 2)
X_train = np.r_[X + 2, X - 2]
# Generate new normal (not abnormal) observations
X = 0.3 * np.random.randn(20, 2)
X_test = np.r_[X + 2, X - 2]
# Generate some abnormal novel observations
X_outliers = np.random.uniform(low=-4, high=4, size=(20, 2))

# fit the model for novelty detection (novelty=True)
clf = LocalOutlierFactor(n_neighbors=20, novelty=True, contamination=0.1)
clf.fit(X_train)
# DO NOT use predict, decision_function and score_samples on X_train as this
# would give wrong results but only on new unseen data (not used in X_train),
# e.g. X_test, X_outliers or the meshgrid
y_pred_test = clf.predict(X_test)
y_pred_outliers = clf.predict(X_outliers)
n_error_test = y_pred_test[y_pred_test == -1].size
n_error_outliers = y_pred_outliers[y_pred_outliers == 1].size

# plot the learned frontier, the points, and the nearest vectors to the plane
Z = clf.decision_function(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

plt.title("Novelty Detection with LOF")
plt.contourf(xx, yy, Z, levels=np.linspace(Z.min(), 0, 7), cmap=plt.cm.PuBu)
a = plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors="darkred")
plt.contourf(xx, yy, Z, levels=[0, Z.max()], colors="palevioletred")

s = 40
b1 = plt.scatter(X_train[:, 0], X_train[:, 1], c="white", s=s, edgecolors="k")
b2 = plt.scatter(X_test[:, 0], X_test[:, 1], c="blueviolet", s=s, edgecolors="k")
c = plt.scatter(X_outliers[:, 0], X_outliers[:, 1], c="gold", s=s, edgecolors="k")
plt.axis("tight")
plt.xlim((-5, 5))
plt.ylim((-5, 5))
plt.legend(
    [mlines.Line2D([], [], color="darkred"), b1, b2, c],
    [
        "learned frontier",
        "training observations",
        "new regular observations",
        "new abnormal observations",
    ],
    loc=(1.05, 0.4),
    prop=matplotlib.font_manager.FontProperties(size=11),
)
plt.xlabel(
    "errors novel regular: %d/40 ; errors novel abnormal: %d/40"
    % (n_error_test, n_error_outliers)
)
plt.tight_layout()
plt.show()