Cluster evaluation metrics in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Silhouette Score Interpretation

Which statement best describes what a Silhouette Score close to +1 indicates about a clustering result?

A Clusters have many outliers and points are far from cluster centers

B Clusters are overlapping heavily and points are assigned randomly

C Clusters are well separated and points are appropriately assigned to their clusters

D Clusters are too small and have very few points

💡 Hint

Think about what a high Silhouette Score means for the distance between points and their own cluster versus other clusters.

A Silhouette Score near +1 means points are much closer to their own cluster than to other clusters, indicating good separation and assignment.

❓ Predict Output

intermediate

Output of Adjusted Rand Index Calculation

What is the output of the following Python code snippet using sklearn.metrics.adjusted_rand_score?

ML Python

from sklearn.metrics import adjusted_rand_score
labels_true = [0, 0, 1, 1, 2, 2]
labels_pred = [1, 1, 0, 0, 2, 2]
score = adjusted_rand_score(labels_true, labels_pred)
print(round(score, 2))

A 1.0

B 0.0

C -1.0

D 0.5

💡 Hint

Adjusted Rand Index is symmetric and equals 1 when clusterings are identical up to label permutation.

The predicted labels are a perfect permutation of the true labels, so the Adjusted Rand Index is 1.0.

❓ Model Choice

advanced

Choosing the Best Metric for Clustering with Unknown Labels

You have unlabeled data and want to evaluate your clustering algorithm's quality. Which metric is most appropriate?

A Adjusted Rand Index

B Silhouette Score

C Normalized Mutual Information

D Accuracy

💡 Hint

Consider which metrics require true labels and which do not.

Silhouette Score does not require true labels and measures how well clusters are separated internally.

❓ Metrics

advanced

Interpreting Davies-Bouldin Index Values

Which of the following statements about the Davies-Bouldin Index (DBI) is true?

A Lower DBI values indicate better clustering with compact and well-separated clusters

B Higher DBI values indicate better clustering quality

C DBI values range from 0 to 1, where 1 is perfect clustering

D DBI is only valid for binary clustering problems

💡 Hint

Think about what a low versus high DBI means for cluster similarity and separation.

A lower Davies-Bouldin Index means clusters are compact and far from each other, indicating better clustering.

🔧 Debug

expert

Identifying the Error in Cluster Evaluation Code

What error will the following code raise when executed?

ML Python

from sklearn.metrics import silhouette_score
X = [[1, 2], [2, 3], [10, 10], [11, 11]]
labels = [0, 0, 1]
score = silhouette_score(X, labels)
print(score)

A No error, prints a float score

B TypeError: silhouette_score() missing required positional argument

C IndexError: list index out of range

D ValueError: Number of labels does not match number of samples

💡 Hint

Check if the number of labels matches the number of data points.

The labels list has fewer elements than the data points, causing a ValueError.

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