Cluster evaluation metrics in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of cluster evaluation metrics?

Cluster evaluation metrics help us measure how well a clustering algorithm has grouped data points. They tell us if clusters are tight and well-separated.

beginner

Explain the Silhouette Score in clustering.

The Silhouette Score measures how similar a point is to its own cluster compared to other clusters. Scores range from -1 to 1, where a higher score means better clustering.

intermediate

What does the Davies-Bouldin Index indicate?

The Davies-Bouldin Index measures the average similarity between clusters. Lower values mean clusters are more distinct and better separated.

intermediate

How does the Calinski-Harabasz Index evaluate clusters?

The Calinski-Harabasz Index compares the variance within clusters to the variance between clusters. Higher values indicate better defined clusters.

intermediate

What is the difference between internal and external cluster evaluation metrics?

Internal metrics use only the data and cluster labels to evaluate quality (e.g., Silhouette Score). External metrics compare clustering results to known true labels (e.g., Adjusted Rand Index).

Which cluster evaluation metric ranges from -1 to 1 and measures how well points fit their clusters?

A Calinski-Harabasz Index

B Davies-Bouldin Index

C Adjusted Rand Index

D Silhouette Score

The Silhouette Score ranges from -1 to 1 and measures how similar points are to their own cluster compared to others.

A lower value of which metric indicates better cluster separation?

A Davies-Bouldin Index

B Silhouette Score

C Calinski-Harabasz Index

D Adjusted Rand Index

The Davies-Bouldin Index measures cluster similarity; lower values mean clusters are more distinct.

Which metric compares variance within clusters to variance between clusters?

A Calinski-Harabasz Index

B Silhouette Score

C Davies-Bouldin Index

D Adjusted Rand Index

The Calinski-Harabasz Index evaluates clustering by comparing within-cluster and between-cluster variance.

Which cluster evaluation metric requires true labels to compare clustering results?

A Calinski-Harabasz Index

B Davies-Bouldin Index

C Adjusted Rand Index

D Silhouette Score

The Adjusted Rand Index is an external metric that compares clustering to true labels.

Internal cluster evaluation metrics use:

A Random data

B Only data and cluster labels

C External validation data

D True labels only

Internal metrics evaluate clusters using only the data and the cluster assignments.

Describe the Silhouette Score and how it helps evaluate clusters.

Think about how close points are to their own cluster versus others.

Explain the difference between internal and external cluster evaluation metrics.

Consider whether true labels are needed.

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