Cluster evaluation metrics in SciPy - Step-by-Step Execution

Concept Flow - Cluster evaluation metrics

Start with true labels and predicted clusters

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Choose evaluation metric

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Calculate metric value

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Interpret metric: higher or lower is better

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Use metric to compare clustering quality

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End

We start with true and predicted cluster labels, pick a metric, calculate it, then interpret the result to judge clustering quality.

Execution Sample

SciPy

from sklearn.metrics import adjusted_rand_score
true = [0, 0, 1, 1, 2, 2]
pred = [0, 0, 2, 1, 2, 2]
score = adjusted_rand_score(true, pred)
print(score)

Calculate Adjusted Rand Index to compare true and predicted cluster labels.

Execution Table

Step	Action	Input	Intermediate Result	Output
1	Input true labels	[0, 0, 1, 1, 2, 2]	-	Stored true labels
2	Input predicted labels	[0, 0, 2, 1, 2, 2]	-	Stored predicted labels
3	Calculate contingency matrix	true & pred	[[2, 0, 0], [0, 1, 1], [0, 0, 2]]	Contingency matrix computed
4	Compute index components	contingency matrix	Sum combinations for pairs	Pairs counted
5	Calculate Adjusted Rand Index	index components	Adjusted for chance	Score = 0.5757575757575757
6	Print score	score	-	0.5757575757575757
7	End	-	-	Execution complete

💡 All steps completed, Adjusted Rand Index calculated and printed

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 5	Final
true	None	[0, 0, 1, 1, 2, 2]	[0, 0, 1, 1, 2, 2]	[0, 0, 1, 1, 2, 2]	[0, 0, 1, 1, 2, 2]	[0, 0, 1, 1, 2, 2]
pred	None	None	[0, 0, 2, 1, 2, 2]	[0, 0, 2, 1, 2, 2]	[0, 0, 2, 1, 2, 2]	[0, 0, 2, 1, 2, 2]
contingency_matrix	None	None	None	[[2, 0, 0], [0, 1, 1], [0, 0, 2]]	[[2, 0, 0], [0, 1, 1], [0, 0, 2]]	[[2, 0, 0], [0, 1, 1], [0, 0, 2]]
score	None	None	None	None	0.5757575757575757	0.5757575757575757

Key Moments - 3 Insights

Why is the Adjusted Rand Index not 1 even though some clusters match?

Because the metric adjusts for chance grouping, partial mismatches lower the score as shown in step 5 of the execution table.

What does the contingency matrix represent in clustering evaluation?

It counts how many points fall into each pair of true and predicted clusters, as shown in step 3 of the execution table.

Why do we need both true and predicted labels as inputs?

Because cluster evaluation metrics compare these two label sets to measure similarity, as shown in steps 1 and 2.

Visual Quiz - 3 Questions

Look at the execution table at step 5, what is the Adjusted Rand Index score calculated?

A 0.0

B 1.0

C 0.5757575757575757

D 0.85

💡 Hint

Refer to the 'Output' column in step 5 of the execution_table.

At which step is the contingency matrix computed?

A Step 3

B Step 2

C Step 4

D Step 5

💡 Hint

Check the 'Action' column in the execution_table for when the contingency matrix is created.

If the predicted labels were identical to true labels, what would the Adjusted Rand Index be?

A Negative

B Exactly 1

C Close to 0

D Undefined

💡 Hint

Adjusted Rand Index equals 1 when clustering matches perfectly, as explained in key_moments.

Concept Snapshot

Cluster evaluation metrics compare true and predicted cluster labels.
Common metrics: Adjusted Rand Index, Silhouette Score, Homogeneity.
Input: true labels and predicted labels.
Output: score indicating clustering quality.
Higher score usually means better clustering.
Use metrics to choose or tune clustering methods.

Full Transcript

Cluster evaluation metrics help us measure how well our clustering matches the true groups. We start with two lists: true labels and predicted cluster labels. We pick a metric like Adjusted Rand Index, which compares these labels and adjusts for chance. The code calculates a contingency matrix counting overlaps between true and predicted clusters. Then it computes the score, which ranges from -1 to 1, where 1 means perfect match. The example shows a score of about 0.58, meaning partial agreement. This process helps us judge clustering quality and improve models.