Clustering Evaluation — Interview Grill

35 questions on internal/external metrics, choosing K, stability. Drill until you can answer 24+ cold.

A. Internal metrics

1. Silhouette score formula? $s(i)=(b-a)/\max (a,b)$. $a$ intra-cluster mean dist, $b$ nearest-other-cluster mean dist.

2. Silhouette range? $[-1,1]$. Negative = misclassified.

3. Davies-Bouldin intuition? Average over clusters of (spread + spread of nearest other) / distance to nearest other. Lower = better.

4. Calinski-Harabasz intuition? Variance ratio: between-cluster / within-cluster. Higher = better.

5. Dunn index? Min inter-cluster distance / max intra-cluster diameter. Higher = better. Sensitive to outliers.

6. Why do internal metrics favor globular clusters? They reward compactness + separation — the structure K-means produces. Tautological with K-means.

7. Internal metric range? Silhouette: $[-1,1]$. DB: $[0,\infty )$ lower better. CH: $[0,\infty )$ higher better. Dunn: $[0,\infty )$ higher better.

B. External metrics

8. Adjusted Rand Index range? $[-1,1]$. 1 perfect; 0 chance; negative worse than chance.

9. ARI core idea? Pair-based: fraction of pairs consistently classified (same vs different), corrected for chance.

10. NMI definition? Mutual information / mean entropy. $[0,1]$.

11. NMI vs ARI — main difference? NMI: doesn't penalize having more / fewer clusters than classes. ARI: pair-based, more sensitive to cardinality.

12. V-measure components? Homogeneity (each cluster = 1 class) + completeness (each class = 1 cluster). Harmonic mean.

13. Purity formula? $\frac{1}{N}{\sum }_k{\max }_l|C_k\cap L_l|$. Majority label per cluster.

14. Purity bias? Trivially high with many small clusters. Always check completeness.

15. Pairwise F-measure? Precision/recall over pairs (same cluster, same class). Pairwise version of standard F1.

C. Choosing K

16. Elbow method? Plot WCSS vs $K$. Look for "elbow" (kink). Subjective.

17. Issue with elbow? Often no clear elbow; varies with cluster sizes; subjective.

18. Silhouette method for K? Compute silhouette for various $K$; pick max.

19. Gap statistic? Compare WCSS to expected under uniform reference. Pick $K$ where gap is largest. Statistically grounded; expensive.

20. Stability-based K selection? Bootstrap data, rerun clustering. Pick $K$ with most consistent assignments across bootstraps.

21. BIC for K (in GMM)? Yes — likelihood-based information criterion. Picks $K$ balancing fit and complexity.

22. Should K equal number of true classes? Not necessarily. Classes may not match natural cluster structure.

D. Stability and validation

23. Bootstrap stability procedure? Resample data, rerun clustering, compute ARI between bootstrap and original. High ARI → stable.

24. Initialization stability? Run K-means with different seeds. High variance → init-sensitive solution.

25. Visualization tools for clustering? PCA, t-SNE, UMAP for 2D projection. Visually inspect.

26. Why does visualization help? Catches obvious failures (one giant cluster + many tiny; clusters that aren't separable).

27. Downstream task validation? If clustering serves a use case (segmentation, anomaly), evaluate via that task. The most reliable validation.

E. Common pitfalls

28. Comparing different algorithms with internal metrics? Often unfair — different $K$, different cluster shapes. Watch out.

29. Internal metric for K-means + silhouette = good? Tautological. Both favor compact globular clusters.

30. Ignoring outliers? DBSCAN flags them; K-means absorbs. Affects all metrics differently.

31. Trusting one run? K-means is init-sensitive. Use k-means++ + multiple runs + report best.

32. Reporting only mean metric? Report variance across seeds / bootstraps. Single number misleads.

F. Advanced

33. Cluster validity in high-dim? Curse of dimensionality: distances become uniform. Internal metrics break down. Use dimensionality reduction first.

34. Soft clustering evaluation? Soft (GMM) needs different metrics: NLL on held-out, soft V-measure, etc.

35. Hierarchical clustering evaluation? Cophenetic correlation: correlation between original distances and dendrogram distances. Higher = dendrogram preserves geometry.

Quick fire

36. Silhouette range? $[-1,1]$. 37. ARI chance value? 0. 38. NMI range? $[0,1]$. 39. DB lower or higher better? Lower. 40. CH lower or higher? Higher. 41. Gap statistic compares to? Uniform reference. 42. Best K choice strategy? Multiple methods + downstream validation. 43. V-measure components? Homogeneity + completeness. 44. Purity bias? High with many small clusters. 45. Stability test? Bootstrap + ARI.

Self-grading

If you can't answer 1-15, you don't know clustering metrics. If you can't answer 16-30, you'll struggle on K-selection / validation. If you can't answer 31-45, frontier-lab questions on rigorous unsupervised eval will go past you.

Aim for 28+/45 cold.