Flat clustering (fcluster) in SciPy - Step-by-Step Execution

Concept Flow - Flat clustering (fcluster)

Start with hierarchical clustering result

↓

Choose a threshold or criterion

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Call fcluster to assign cluster labels

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Get flat clusters as output

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Use clusters for analysis or visualization

Flat clustering cuts a hierarchical clustering tree at a chosen level to assign cluster labels to data points.

Execution Sample

SciPy

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

X = np.array([[1,2],[2,2],[8,7],[8,8]])
Z = linkage(X, 'single')
clusters = fcluster(Z, t=3, criterion='distance')

This code clusters 4 points hierarchically and then cuts the tree at distance 3 to assign flat cluster labels.

Execution Table

Step	Action	Input/Condition	Output/Result
1	Create data points	X = [[1,2],[2,2],[8,7],[8,8]]	X array created
2	Compute linkage	method='single'	Z linkage matrix with merges and distances
3	Call fcluster	Z linkage, t=3, criterion='distance'	Assign cluster labels based on distance threshold
4	Output clusters	clusters array	[1, 1, 2, 2]
5	End	All points assigned clusters	Flat clustering complete

💡 All points assigned to clusters based on distance threshold 3

Variable Tracker

Variable	Start	After linkage	After fcluster	Final
X	[[1,2],[2,2],[8,7],[8,8]]	[[1,2],[2,2],[8,7],[8,8]]	[[1,2],[2,2],[8,7],[8,8]]	[[1,2],[2,2],[8,7],[8,8]]
Z	None	Linkage matrix with shape (3,4)	Same	Same
clusters	None	None	[1,1,2,2]	[1,1,2,2]

Key Moments - 3 Insights

Why do some points get the same cluster label?

Because their distance in the linkage tree is below the threshold t=3, so fcluster groups them together (see execution_table step 4).

What does the 't' parameter control in fcluster?

It sets the maximum distance to cut the hierarchical tree; points joined below this distance share the same cluster label (execution_table step 3).

Why do we need the linkage matrix Z before calling fcluster?

Z contains the hierarchical clustering info (merges and distances) that fcluster uses to assign flat clusters (execution_table step 2 and 3).

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what cluster label is assigned to the point [8,8]?

A 3

B 1

C 2

D 4

💡 Hint

Check the clusters array in execution_table step 4; the last point corresponds to label 2.

At which step does the hierarchical linkage matrix get created?

A Step 2

B Step 3

C Step 1

D Step 4

💡 Hint

Look at execution_table step 2 where linkage is computed.

If we change t=1 in fcluster, what happens to the clusters output?

A All points get the same cluster label

B Each point gets a unique cluster label

C Clusters remain the same as with t=3

D fcluster raises an error

💡 Hint

With t=1, only points joined at distance <=1 are clustered together; since some points are farther apart, this results in more clusters, possibly unique labels per point.

Concept Snapshot

Flat clustering with fcluster:
- Input: linkage matrix from hierarchical clustering
- Parameter t: distance threshold to cut tree
- Output: cluster labels array
- Points joined below t share cluster
- Use for simple cluster assignment from hierarchy

Full Transcript

Flat clustering with fcluster takes a hierarchical clustering result and cuts it at a chosen distance threshold to assign cluster labels. First, data points are clustered hierarchically using linkage. Then, fcluster uses the linkage matrix and a threshold t to assign flat cluster labels. Points connected below the threshold get the same label. This method helps convert a hierarchical tree into simple clusters for analysis or visualization.