Outlier Detection with LOF

Introduction

The Local Outlier Factor (LOF) algorithm is an unsupervised machine learning method that is used to detect anomalies in data. It computes the local density deviation of a given data point with respect to its neighbors and considers as outliers the samples that have a substantially lower density than their neighbors.

In this lab, we will use LOF to detect outliers in a dataset.

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Skills Graph

Import Libraries

We will import numpy and matplotlib for data manipulation and visualization respectively. We will also import LocalOutlierFactor from sklearn.neighbors for outlier detection.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.neighbors import LocalOutlierFactor

Generate Data with Outliers

We will generate a dataset of 120 data points with 100 inliers and 20 outliers. We will then plot the data to visualize the outliers.

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]

plt.scatter(X[:, 0], X[:, 1], color="k", s=3.0)
plt.axis("tight")
plt.xlim((-5, 5))
plt.ylim((-5, 5))
plt.xlabel("Data points")
plt.title("Data with Outliers")
plt.show()

Fit the Model for Outlier Detection

We will use LocalOutlierFactor to fit the model for outlier detection and compute the predicted labels of the training samples.

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

Plot Results

We will plot the data points with circles whose radius is proportional to the outlier scores.

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("Outlier Detection")
plt.legend(
    handler_map={scatter: HandlerPathCollection(update_func=update_legend_marker_size)}
)
plt.title("Local Outlier Factor (LOF)")
plt.show()

Summary

In this lab, we have learned how to use Local Outlier Factor (LOF) for outlier detection. We have generated a dataset with outliers, fit the model for outlier detection, and plotted the results. LOF is a powerful unsupervised machine learning method that can be used to detect anomalies in a wide range of applications.