Cluster-based local outlier factor

As explained in Outlier Detection in Python

Cluster-based local outlier factor is an outlier detection algorithm that scores observations using cluster membership, cluster size, and distance to relevant clusters.

Cluster-based local outlier factor (CBLOF) detects outliers by combining cluster membership with distance to relevant cluster centers. It is especially useful when records form meaningful groups and outlierness is better judged relative to those groups than to the full dataset. section 6.6 section 7.8

CBLOF proceeds through several practical decisions:

• Cluster every observation, commonly with K-means in PyOD, although any clustering algorithm may be used. section 6.6
• Label clusters as large or small using tunable alpha and beta parameters. section 6.6
• Score points in large clusters by their distance to the cluster center; evaluate points in small clusters relative to the nearest large cluster center. section 6.6
• Use PyOD’s default nearest-large-center distance, or include cluster sizes with use_weights for behavior closer to the original formulation. section 6.6

Small and large clusters

With three clusters, C1, C2, and C3, points in the small C3 cluster may be scored against the nearby large C2 center even when they lie close to C3’s own center. This reflects the possibility that C3 is a subcluster or a clustering artifact. section 6.6

CBLOF depends on the clustering quality. Extreme values can distort clustering and cause masking or swamping; adding ten extreme training values reduced a reported AUROC from 0.79 to 0.52. Cleaning strong outliers beforehand and testing detector robustness are therefore important. section 8.5.5

Figure 6.12 The idea behind CBLOF. The data is divided into three clusters, C1, C2, and C3. As C3 is a small cluster, it can be more reasonable to evaluate the points in C3 relative to the closest large cluster, C2. Given a different clustering of this data, these points could have been included in C2 in any case.

Compare the three-cluster arrangement visually to see why a small cluster may be evaluated against a nearby large cluster rather than its own center. section 6.6

How Outlier Detection in Python covers it

How deep it goes

Explains clustering, size labeling, score distances, implementation defaults, and robustness limitations without deriving the full scoring formula.

Examples

Uses three illustrative clusters, injected extreme values, and abalone timing experiments to examine interpretation, robustness, and performance.

What it assumes

Requires choosing a clustering algorithm and interpreting cluster sizes, while allowing clustering methods beyond PyOD’s K-means default.

What you can do after

Apply it via PyOD by fitting clusters, selecting size thresholds, scoring records, and testing sensitivity to contaminated training data.

How it connects

Connects clustering with DBSCAN, Gaussian mixture models, local outlier factor, and cluster-wise outlier detection.

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Related concepts

• area under the curvemeasured by · The area under a curve is the integral of its values over a specified domain and, in classification evaluation, commonly summarizes performance across decision thresholds.
• K-means clusteringuses · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
• local outlier factorkind of · Local Outlier Factor is a density-based anomaly-detection algorithm that scores an observation by comparing its local density with those of its neighbors.
• clusteringuses · Clustering is the technique of grouping data items according to similarity or shared characteristics.
• mahalanobis distancecontrasts with · Mahalanobis distance is a covariance-adjusted measure of separation between observations or between an observation and a reference distribution.
• outlier detectionkind of · Outlier detection is the process of identifying observations that substantially deviate from an expected or prevailing pattern in data.

This explainer was generated by Manning's knowledge graph from the text of Outlier Detection in Python. The section links point to the parts of the book it draws on.