Cluster evaluation metrics in SciPy

Introduction

Cluster evaluation metrics help us check how good our groups (clusters) are. They tell us if the data points in each group are close and if different groups are well separated.

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

To check if your clustering of images puts similar images in the same group.

When comparing different clustering methods to pick the best one.

To measure how well your clustering matches known labels (if available).

When tuning clustering settings to improve group quality.

Syntax

SciPy

from sklearn.metrics import silhouette_score, adjusted_rand_score, davies_bouldin_score

# silhouette_score(X, labels)
# adjusted_rand_score(true_labels, predicted_labels)
# davies_bouldin_score(X, labels)

These functions need your data points (X) and cluster labels.

Some metrics need true labels to compare, others work without them.

Examples

Measures how close points in a cluster are compared to other clusters. Values near 1 mean good clusters.

SciPy

silhouette_score(X, labels)

Compares your clustering to known labels. 1 means perfect match, 0 means random.

SciPy

adjusted_rand_score(true_labels, predicted_labels)

Lower values mean better clusters with less overlap.

SciPy

davies_bouldin_score(X, labels)

Sample Program

This code creates fake data with 3 groups, clusters it, and then checks how good the clustering is using three metrics.

SciPy

from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score, adjusted_rand_score, davies_bouldin_score

# Create sample data with 3 clusters
X, true_labels = make_blobs(n_samples=300, centers=3, cluster_std=0.60, random_state=0)

# Cluster data using KMeans
kmeans = KMeans(n_clusters=3, random_state=0)
predicted_labels = kmeans.fit_predict(X)

# Calculate metrics
sil_score = silhouette_score(X, predicted_labels)
ari_score = adjusted_rand_score(true_labels, predicted_labels)
db_score = davies_bouldin_score(X, predicted_labels)

print(f"Silhouette Score: {sil_score:.3f}")
print(f"Adjusted Rand Index: {ari_score:.3f}")
print(f"Davies-Bouldin Score: {db_score:.3f}")

Important Notes

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

Adjusted Rand Index needs true labels; if unknown, use unsupervised metrics like silhouette.

Davies-Bouldin score is better when smaller.

Summary

Cluster evaluation metrics help measure how well your data is grouped.

Use silhouette score and Davies-Bouldin score when true labels are unknown.

Use Adjusted Rand Index to compare clustering with known labels.

Practice

1. Which cluster evaluation metric is best used when you do NOT have true labels for your data?

easy

A. Adjusted Rand Index

B. Silhouette Score

C. Accuracy Score

D. Mean Squared Error

Solution

1. Step 1: Understand the role of true labels

   Adjusted Rand Index requires true labels to compare clusters, so it is not suitable without labels.

2. Step 2: Identify metrics for unknown labels

   Silhouette Score measures how well clusters are separated without needing true labels.

3. Final Answer:

   Silhouette Score -> Option B

4. Quick Check:

   Unknown labels = Silhouette Score [OK]

Hint: Use silhouette score when labels are unknown [OK]

Common Mistakes:

• Confusing Adjusted Rand Index as label-free
• Choosing accuracy score which needs labels
• Using mean squared error for clustering

2. Which of the following is the correct way to import the silhouette_score function for cluster evaluation?

easy

A. from scipy.cluster import silhouette_score

B. from scipy.spatial.distance import silhouette_score

C. from scipy.cluster.hierarchy import silhouette_score

D. from sklearn.metrics import silhouette_score

Solution

1. Step 1: Check common library modules

   Silhouette score is available in sklearn.metrics module, not in scipy.cluster or spatial.distance.

2. Step 2: Verify import syntax

   The correct import is from sklearn.metrics import silhouette_score.

3. Final Answer:

   from sklearn.metrics import silhouette_score -> Option D

4. Quick Check:

   Correct import = sklearn.metrics [OK]

Hint: Silhouette score is in sklearn.metrics module [OK]

Common Mistakes:

• Importing from scipy.cluster directly
• Using scipy.spatial.distance for silhouette_score
• Confusing hierarchy module with vq

3. What is the output of the following code snippet?

from scipy.cluster.vq import kmeans, vq, whiten
import numpy as np

data = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])
whitened = whiten(data)
centroids, _ = kmeans(whitened, 2)
cluster_labels, _ = vq(whitened, centroids)
from sklearn.metrics import silhouette_score
score = silhouette_score(whitened, cluster_labels)
print(round(score, 2))

medium

A. 0.75

B. 1.00

C. 0.35

D. 0.55

Solution

1. Step 1: Understand the code flow

   The code whitens data, runs kmeans for 2 clusters, assigns labels, then calculates silhouette score.

2. Step 2: Interpret silhouette score meaning

   Data clearly forms two groups; silhouette score is around 0.75 indicating good cluster separation.

3. Final Answer:

   0.75 -> Option A

4. Quick Check:

   Well-separated clusters ≈ 0.75 silhouette [OK]

Hint: Silhouette near 0.75 means good cluster separation [OK]

Common Mistakes:

• Expecting silhouette score of 1.0 always
• Confusing whitened data with original scale
• Misreading cluster labels

4. Identify the error in this code snippet for calculating Davies-Bouldin score:

from scipy.spatial.distance import davies_bouldin_score

labels = [0, 0, 1, 1]
data = [[1, 2], [1, 4], [10, 2], [10, 4]]
score = davies_bouldin_score(data, labels)
print(score)

medium

A. Data must be a numpy array, not list

B. Labels and data length mismatch

C. Importing davies_bouldin_score from wrong module

D. Davies-Bouldin score requires true labels

Solution

1. Step 1: Check import source

   Davies-Bouldin score is in sklearn.metrics, not scipy.spatial.distance.

2. Step 2: Validate data and labels

   Data and labels lengths match and data as list works with sklearn, so no error there.

3. Final Answer:

   Importing davies_bouldin_score from wrong module -> Option C

4. Quick Check:

   Correct import is sklearn.metrics [OK]

Hint: Davies-Bouldin score is in sklearn.metrics, not scipy [OK]

Common Mistakes:

• Importing from scipy.spatial.distance
• Assuming data must be numpy array
• Thinking Davies-Bouldin needs true labels

5. You have true labels and predicted cluster labels for a dataset. Which metric from scipy or sklearn should you use to evaluate clustering quality by comparing these labels?

hard

A. Adjusted Rand Index

B. Davies-Bouldin Score

C. Silhouette Score

D. Calinski-Harabasz Index

Solution

1. Step 1: Identify metrics needing true labels

   Adjusted Rand Index compares predicted clusters with true labels to measure similarity.

2. Step 2: Exclude label-free metrics

   Silhouette, Davies-Bouldin, and Calinski-Harabasz do not use true labels for evaluation.

3. Final Answer:

   Adjusted Rand Index -> Option A

4. Quick Check:

   True vs predicted labels = Adjusted Rand Index [OK]

Hint: Use Adjusted Rand Index to compare true and predicted labels [OK]

Common Mistakes:

• Using silhouette score with true labels
• Confusing Davies-Bouldin as label-based
• Choosing Calinski-Harabasz for label comparison