Dendrogram visualization in SciPy - Step-by-Step Execution

Concept Flow - Dendrogram visualization

Start with data points

↓

Calculate distances

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Perform hierarchical clustering

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Create linkage matrix

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Plot dendrogram

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Visualize cluster merges

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End

This flow shows how data points are clustered step-by-step and visualized as a dendrogram.

Execution Sample

SciPy

from scipy.cluster.hierarchy import dendrogram, linkage
import matplotlib.pyplot as plt

X = [[1, 2], [3, 4], [5, 6], [7, 8]]
Z = linkage(X, 'single')
dendrogram(Z)
plt.show()

This code clusters 4 points and plots their dendrogram showing merges.

Execution Table

Step	Action	Data/Variables	Result/Output
1	Input data points	X = [[1,2],[3,4],[5,6],[7,8]]	Data ready for clustering
2	Calculate linkage matrix	linkage(X, 'single')	Z = [[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]
3	Plot dendrogram	dendrogram(Z)	Dendrogram plot shows cluster merges
4	Show plot	plt.show()	Visual dendrogram displayed
5	End		Process complete

💡 All data points clustered and dendrogram displayed

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
X	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]	[[1,2],[3,4],[5,6],[7,8]]
Z	None	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]	[[0,1,2.8284271247461903,2],[2,3,2.8284271247461903,2],[4,5,2.8284271247461903,4]]

Key Moments - 3 Insights

Why does the linkage matrix Z have 3 rows for 4 data points?

Because hierarchical clustering merges points step-by-step, for n points there are n-1 merges, so Z has n-1 rows (3 rows for 4 points). See execution_table step 2.

What does each row in the linkage matrix represent?

Each row shows a merge: the two clusters merged, the distance between them, and the number of original points in the new cluster. This is shown in execution_table step 2.

Why do we use 'single' linkage in linkage()?

'Single' linkage means clusters are merged based on the smallest distance between points in clusters. This affects the shape of the dendrogram, as seen in execution_table step 2.

Visual Quiz - 3 Questions

Look at the execution_table step 2, what does the number 2.828 represent in the linkage matrix?

A The index of a data point

B The number of clusters

C The distance between two clusters merged

D The height of the dendrogram

💡 Hint

Check the 'Result/Output' column in step 2 of execution_table where linkage matrix is shown.

At which step is the dendrogram plot created according to the execution_table?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Action' column for plotting dendrogram in execution_table.

If we add more data points, how will the linkage matrix Z change?

A It will have fewer rows

B It will have more rows

C It will stay the same size

D It will become empty

💡 Hint

Recall from key_moments that linkage matrix has n-1 rows for n points.

Concept Snapshot

Dendrogram visualization:
- Use scipy.cluster.hierarchy linkage() to cluster data
- linkage() returns a matrix showing cluster merges
- dendrogram() plots this matrix as a tree
- Each merge shows which clusters joined and distance
- Visualizes hierarchical clustering step-by-step

Full Transcript

We start with data points and calculate distances between them. Then we perform hierarchical clustering using linkage() which returns a matrix showing how clusters merge step-by-step. This matrix is passed to dendrogram() to create a tree plot. The dendrogram visually shows the order and distance of merges. The process ends when all points are clustered. This helps us understand cluster relationships visually.