Cluster evaluation metrics in ML Python

Introduction

Cluster evaluation metrics help us check how well our groups (clusters) of data points are formed. They tell us if the clusters are tight and well separated.

When you want to see if your clustering grouped similar items together well.

When comparing different clustering methods to pick the best one.

When you want to check if the number of clusters you chose makes sense.

When you want to measure how close points in the same cluster are.

When you want to measure how far apart different clusters are.

Syntax

ML Python

metric_name(true_labels, predicted_labels)

# Example metrics:
# - adjusted_rand_score(true_labels, predicted_labels)
# - silhouette_score(data, predicted_labels)
# - calinski_harabasz_score(data, predicted_labels)
# - davies_bouldin_score(data, predicted_labels)

Some metrics need the original data points and cluster labels, others only need the labels.

True labels are needed only if you have ground truth to compare against.

Examples

Adjusted Rand Index compares predicted clusters to true groups. Score near 1 means good match.

ML Python

from sklearn.metrics import adjusted_rand_score

true_labels = [0, 0, 1, 1, 2, 2]
predicted_labels = [0, 0, 1, 2, 2, 2]
score = adjusted_rand_score(true_labels, predicted_labels)
print(score)

Silhouette score measures how close points are in the same cluster compared to other clusters. Score near 1 is good.

ML Python

from sklearn.metrics import silhouette_score

import numpy as np

data = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])
predicted_labels = [0, 0, 0, 1, 1, 1]
score = silhouette_score(data, predicted_labels)
print(score)

Sample Model

This code clusters simple 2D points into 2 groups using KMeans. Then it calculates three common cluster evaluation scores to check cluster quality.

ML Python

from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score, calinski_harabasz_score, davies_bouldin_score
import numpy as np

# Sample data: 2 groups of points
X = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])

# Create KMeans clustering with 2 clusters
kmeans = KMeans(n_clusters=2, random_state=42)
kmeans.fit(X)
labels = kmeans.labels_

# Calculate cluster evaluation metrics
sil_score = silhouette_score(X, labels)
calinski_score = calinski_harabasz_score(X, labels)
davies_score = davies_bouldin_score(X, labels)

print(f"Silhouette Score: {sil_score:.3f}")
print(f"Calinski-Harabasz Score: {calinski_score:.3f}")
print(f"Davies-Bouldin Score: {davies_score:.3f}")

Important Notes

Silhouette score ranges from -1 to 1; higher is better.

Calinski-Harabasz score is higher when clusters are dense and well separated.

Davies-Bouldin score is lower when clusters are better separated.

Summary

Cluster evaluation metrics help measure how good your clusters are.

Some metrics need true labels, others only need data and cluster labels.

Use multiple metrics to get a full picture of cluster quality.

Practice

1. Which of the following cluster evaluation metrics requires knowing the true labels of the data?

easy

A. Davies-Bouldin Index

B. Silhouette Score

C. Adjusted Rand Index (ARI)

D. Calinski-Harabasz Index

Solution

1. Step 1: Understand metric types

   Some cluster metrics need true labels (external metrics), others only use cluster assignments (internal metrics).

2. Step 2: Identify ARI as external metric

   Adjusted Rand Index compares predicted clusters to true labels, so it requires true labels.

3. Final Answer:

   Adjusted Rand Index (ARI) -> Option C

4. Quick Check:

   External metric = ARI [OK]

Hint: Only ARI needs true labels; others use cluster data alone [OK]

Common Mistakes:

• Confusing Silhouette Score as needing true labels
• Thinking Davies-Bouldin Index requires true labels
• Assuming Calinski-Harabasz Index uses true labels

2. Which of the following is the correct way to compute the Silhouette Score in Python using scikit-learn for data X and cluster labels labels?

easy

A. from sklearn.metrics import silhouette_score
score = silhouette_score(X, labels)

B. from sklearn.cluster import silhouette_score
score = silhouette_score(labels, X)

C. from sklearn.metrics import silhouette_score
score = silhouette_score(labels, X)

D. from sklearn.metrics import silhouette_score
score = silhouette_score(X)

Solution

1. Step 1: Check import source

   Silhouette Score is in sklearn.metrics, not sklearn.cluster.

2. Step 2: Check function parameters

   Function signature is silhouette_score(X, labels), where X is data and labels are cluster assignments.

3. Final Answer:

   from sklearn.metrics import silhouette_score\nscore = silhouette_score(X, labels) -> Option A

4. Quick Check:

   Correct import and parameter order = D [OK]

Hint: Import from metrics and pass data first, labels second [OK]

Common Mistakes:

• Importing silhouette_score from sklearn.cluster
• Swapping data and labels in function call
• Calling silhouette_score with only data

3. Given the following code, what will be the output of the Davies-Bouldin Index?

from sklearn.metrics import davies_bouldin_score
X = [[1, 2], [2, 1], [10, 10], [11, 11]]
labels = [0, 0, 1, 1]
score = davies_bouldin_score(X, labels)
print(round(score, 2))

medium

A. 0.50

B. 1.41

C. 1.00

D. 0.11

Solution

1. Step 1: Understand Davies-Bouldin Index meaning

   Lower values mean better clusters; it measures average similarity between clusters.

2. Step 2: Calculate score using sklearn

   Running the code gives approximately 0.1111, rounded to 0.11.

3. Final Answer:

   0.11 -> Option D

4. Quick Check:

   Davies-Bouldin score ≈ 0.11 [OK]

Hint: Run sklearn function and round result to 2 decimals [OK]

Common Mistakes:

• Confusing Davies-Bouldin with Silhouette Score values
• Rounding incorrectly
• Misinterpreting higher score as better

4. The following code throws an error. What is the most likely cause?

from sklearn.metrics import silhouette_score
X = [[1, 2], [2, 1], [10, 10], [11, 11]]
labels = [0, 0, 1]
score = silhouette_score(X, labels)
print(score)

medium

A. Mismatch in length between X and labels

B. silhouette_score requires true labels, not cluster labels

C. X should be a numpy array, not a list

D. silhouette_score cannot handle more than 3 clusters

Solution

1. Step 1: Check input lengths

   Data X has 4 samples, but labels list has only 3 elements, causing mismatch error.

2. Step 2: Understand silhouette_score input requirements

   silhouette_score requires labels length equal to number of samples in X.

3. Final Answer:

   Mismatch in length between X and labels -> Option A

4. Quick Check:

   Length mismatch error = A [OK]

Hint: Ensure labels length matches data samples count [OK]

Common Mistakes:

• Thinking silhouette_score needs true labels
• Assuming lists instead of arrays cause error
• Believing cluster count limits cause error

5. You have clustered customer data into 3 groups but want to evaluate cluster quality without true labels. Which combination of metrics gives the best overall insight?

hard

A. Adjusted Rand Index and Calinski-Harabasz Index

B. Silhouette Score and Davies-Bouldin Index

C. Homogeneity Score and Completeness Score

D. Adjusted Mutual Information and Silhouette Score

Solution

1. Step 1: Identify metrics that do not require true labels

   Silhouette Score and Davies-Bouldin Index are internal metrics needing only data and cluster labels.

2. Step 2: Understand other metrics need true labels

   Adjusted Rand Index, Homogeneity, Completeness, and Adjusted Mutual Information require true labels, which are unavailable.

3. Final Answer:

   Silhouette Score and Davies-Bouldin Index -> Option B

4. Quick Check:

   Internal metrics only = A [OK]

Hint: Use only internal metrics when true labels are missing [OK]

Common Mistakes:

• Choosing metrics that require true labels
• Using only one metric instead of combination
• Confusing internal and external metrics