How can we handle anomaly detection with respect to variable density clusters in an unsupervised algorithm like k-means?

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Let’s break down what the question is asking: handling anomaly detection when clusters have variable density in an unsupervised setting like k-means.
Option 1: Remove objects which most improve the clustering objective function
- This is generally problematic. If you remove objects that improve the objective, you’re biasing the dataset and potentially discarding genuine structure, which can distort anomaly detection rather than helping it. It also contradicts the idea of evaluating anomalies without altering the underlying data in a biased way.
Option 2: Perform a hill climbing search with multiple initializations
- Running k-means with multiple initializations helps avoid poor local optima in clustering, but it doesn’t directly address variable-density anomalies. It’s a technique to stabilize clustering results, not a method for anomaly detection across regions of differing density. So it’s not a direct solution for the anomaly-density issue.
Option 3: Remove small and far clusters
- Removing small and distant clusters can help when clusters have highly uneven densities, as small, sparse shards may be artifacts or noise rather than meaningful clusters. However, this action risks discarding legitimate sparse clusters, so it must be applied carefully. It can be used as a heuristic to mitigate the impact of density variation, but it has potential downsides if not justified by the data context.
Option 4: Use relative distance instead of absolute distance
- This approach addresses the core issue: in variable-density data, absolute distances can mislead because points in sparse regions can appear far from centers even if they belong to a meaningful cluster. Relative distance measures (e.g., distance to nearest centers, density-aware comparisons) help accommodate density differences and improve anomaly detection by focusing on local relationships rather than global scales.

In summary, option 4 directly targets the density-variation challenge by adjusting the distance metric. Option 3 offers a heuristic that can be useful in some scenarios but carries risk if not applied with care. Options 1 and 2 do not specifically solve the variable-density anomaly problem and can introduce other issues or be only tangentially related to anomaly handling.

COMP90049_2025_SM2 Lecture 22 Anomaly Detection Practice Quiz

How can we handle anomaly detection with respect to variable density clusters in an unsupervised algorithm like k-means?

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