Hierarchical Clustering and Linkage Methods Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Hierarchical Clustering and Linkage Methods short notes for GATE DA: 5 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Hierarchical Clustering

Chapter Journey: Hierarchical Clustering

Distance Metrics & First Merge

Euclidean, Manhattan, Minkowski. How do we measure similarity between two points?

Linkage Methods

Single, Complete, Average, Ward’s. How do we measure distance between clusters?

Dendrograms

Visualizing the hierarchy. Reading the tree.

Cutting the Tree

Deciding the optimal number of clusters

k

The Core Idea: Agglomerative Clustering

Agglomerative Hierarchical Clustering

Intuition: Start with

N

points, each as its own cluster. Merge the nearest pair. Repeat until one cluster remains.

The Process:

Compute pairwise distances between all points.
Find the pair with the minimum distance.
Merge them into a new cluster.
Update the distance matrix (this is where Linkage Methods come in).
Repeat steps 2-4.

Note: This topic focuses on Step 1 and 2: Distance Metrics and identifying the First Merge.

Summary: First Merge Execution Checklist

Use this mental checklist every time you encounter a first-merge problem:

Format: Write $(x, y, z)$ coordinates clearly.
Metric: Identify if the question demands Manhattan or Euclidean distance.
Pairs: List all $(2 N)$ combinations systematically.
Signs: Double-check subtraction of negative numbers (e.g., $- 1 - 3 = - 4$ ).
Compare: Select the strictly smallest distance.
Verify: Ensure you did not mix up the point labels when declaring the final answer.

Quick Revision: Single and Complete Linkage

Key Formulas

Single Linkage:

D_{single} (C_{i}, C_{j}) = x \in C_{i}, y \in C_{j} min D (x, y)

Complete Linkage:

D_{complete} (C_{i}, C_{j}) = x \in C_{i}, y \in C_{j} max D (x, y)

Update after merge:

D (C_{new}, C_{k}) = min

max

D (C_{i}, C_{k})

and

D (C_{j}, C_{k})

Dendrogram: height = merge distance; cut at height

h

to get clusters
Single linkage: chaining effect, elongated clusters
Complete linkage: compact clusters, no chaining

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Hierarchical Clustering and Linkage Methods Short Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Hierarchical Clustering and Linkage Methods short notes for GATE DA: 5 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice

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