Cluster evaluation metrics in SciPy - Mini Project: Build & Apply

Cluster Evaluation Metrics

📖 Scenario: You have grouped customers into clusters based on their shopping behavior. Now, you want to check how good these clusters are by comparing them to known customer groups.

🎯 Goal: Build a small program to calculate cluster evaluation metrics using sklearn. You will create true labels and predicted cluster labels, then compute the Adjusted Rand Index and Normalized Mutual Information scores.

📋 What You'll Learn

Create two lists: true_labels and predicted_labels with exact values

Import adjusted_rand_score and normalized_mutual_info_score from sklearn.metrics

Calculate ari_score using adjusted_rand_score(true_labels, predicted_labels)

Calculate nmi_score using normalized_mutual_info_score(true_labels, predicted_labels)

Print both scores with descriptive text

💡 Why This Matters

🌍 Real World

Cluster evaluation metrics help businesses check if their customer groups or product categories are meaningful and useful.

💼 Career

Data scientists and analysts use these metrics to validate clustering results and improve machine learning models.

1

Create true and predicted cluster labels

Create a list called true_labels with values [0, 0, 1, 1, 2, 2] and a list called predicted_labels with values [0, 0, 2, 1, 2, 2].

SciPy

# Create the true and predicted cluster labels lists
# Your code here

Hint

Use square brackets to create lists with the exact numbers given.

2

Import cluster evaluation functions

Import adjusted_rand_score and normalized_mutual_info_score from sklearn.metrics.

SciPy

true_labels = [0, 0, 1, 1, 2, 2]
predicted_labels = [0, 0, 2, 1, 2, 2]
# Import adjusted_rand_score and normalized_mutual_info_score from sklearn.metrics
# Your code here

Hint

Use from sklearn.metrics import adjusted_rand_score, normalized_mutual_info_score.

3

Calculate ARI and NMI scores

Calculate ari_score by calling adjusted_rand_score(true_labels, predicted_labels) and calculate nmi_score by calling normalized_mutual_info_score(true_labels, predicted_labels).

SciPy

from sklearn.metrics import adjusted_rand_score, normalized_mutual_info_score

true_labels = [0, 0, 1, 1, 2, 2]
predicted_labels = [0, 0, 2, 1, 2, 2]
# Calculate ari_score and nmi_score
# Your code here

Hint

Call the functions with the two lists as arguments and save results in ari_score and nmi_score.

4

Print the cluster evaluation scores

Print the text "Adjusted Rand Index:" followed by ari_score and print the text "Normalized Mutual Information:" followed by nmi_score.

SciPy

from sklearn.metrics import adjusted_rand_score, normalized_mutual_info_score

true_labels = [0, 0, 1, 1, 2, 2]
predicted_labels = [0, 0, 2, 1, 2, 2]

ari_score = adjusted_rand_score(true_labels, predicted_labels)
nmi_score = normalized_mutual_info_score(true_labels, predicted_labels)
# Print the ARI and NMI scores
# Your code here

Hint

Use two print statements with the exact text and variables.

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