Hierarchical clustering (linkage) in SciPy - Step-by-Step Execution

Concept Flow - Hierarchical clustering (linkage)

Start with each point as a cluster

↓

Calculate distances between clusters

↓

Find closest clusters

↓

Merge closest clusters

↓

Update distances

↓

More than one cluster?

No↓

Done

Start with each data point alone, then repeatedly merge the closest clusters until all points form one cluster.

Execution Sample

SciPy

from scipy.cluster.hierarchy import linkage
import numpy as np

points = np.array([[1,2],[2,3],[10,10],[11,11]])
Z = linkage(points, method='single')

This code groups 4 points step-by-step using single linkage hierarchical clustering.

Execution Table

Step	Clusters Merged	Distance	Clusters After Merge	Action
1	[0] and [1]	1.414	[[0,1]] [2] [3]	Merge closest points 0 and 1
2	[2] and [3]	1.414	[[0,1]] [[2,3]]	Merge closest points 2 and 3
3	[[0,1]] and [[2,3]]	12.728	[[0,1,2,3]]	Merge two clusters into one
4	-	-	[[0,1,2,3]]	Only one cluster left, stop

💡 All points merged into a single cluster, clustering complete

Variable Tracker

Variable	Start	After 1	After 2	After 3	Final
clusters	[0], [1], [2], [3]	[[0,1]], [2], [3]	[[0,1]], [[2,3]]	[[0,1,2,3]]	[[0,1,2,3]]
distances	calculated between all points	updated distances between clusters	updated distances between clusters	no distances left	no distances left

Key Moments - 3 Insights

Why do we merge points 0 and 1 first, not 0 and 2?

Because the distance between points 0 and 1 is smaller (1.414) than between 0 and 2 (about 12.04), as shown in step 1 of the execution_table.

What happens to distances after merging clusters?

Distances are recalculated between the new cluster and remaining clusters, as seen after step 1 and 2 in the execution_table where clusters and distances update.

When does the clustering stop?

When only one cluster remains, as shown in step 4 of the execution_table where no more merges happen.

Visual Quiz - 3 Questions

Look at the execution_table, which clusters merge at step 2?

A [2] and [3]

B [[0,1]] and [[2,3]]

C [0] and [1]

D [1] and [2]

💡 Hint

Check the 'Clusters Merged' column at step 2 in the execution_table.

At which step does the condition 'only one cluster left' become true?

A Step 1

B Step 3

C Step 4

D Step 2

💡 Hint

Look at the 'Action' column in the execution_table for when clustering stops.

If we used 'complete' linkage instead of 'single', how would the distance at step 3 change?

A It would be the same

B It would be larger

C It would be smaller

D It would be zero

💡 Hint

Complete linkage uses the farthest points distance, so check the 'Distance' column at step 3.

Concept Snapshot

Hierarchical clustering groups points stepwise.
Start: each point is its own cluster.
Find closest clusters by distance.
Merge them and update distances.
Repeat until one cluster remains.
Linkage method (single, complete) affects distance calculation.

Full Transcript

Hierarchical clustering starts with each data point as its own cluster. We calculate distances between all clusters and merge the closest two. After merging, distances are updated to reflect the new clusters. This repeats until all points form one cluster. The linkage method defines how distances between clusters are measured. In this example, single linkage merges clusters based on the shortest distance between points. The execution table shows each merge step, clusters involved, and distances. The process stops when only one cluster remains.