Clustering

Clustering

1. Goal

Group points so similar together, dissimilar apart — no labels. Use for segmentation, compression, anomaly pre-step.

2. What Makes It Hard

No single definition: compactness vs connectivity vs density give different answers. Must choose $k$ / scale, handle shape, outliers, high-$d$ distances.

3. Families

Family	Idea	Example
Partitional	$k$ centers, assign nearest	$k$-means
Medoid	center = real point	$k$-medoids
Hierarchical	merge / split tree	agglomerative
Density	grow dense regions	DBSCAN (next topics)
Spectral	graph cut	spectral clustering

4. Validation Without Labels

Elbow (kink in distortion vs $k$), silhouette (cohesion vs separation, $-1$ to $+1$), stability across runs.

$a$ = mean intra-cluster distance, $b$ = mean nearest-cluster distance.

5. Exam Points

• Define clustering + challenges — 3-5 marks, frequent.
• Families with one example each — 5 marks, frequent.
• Elbow / silhouette — 3 marks, frequent.