Cluster evaluation metrics in ML Python - 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 groups data points. They tell us if clusters are tight and well-separated.

intermediate

Explain the Silhouette Score in clustering.

The Silhouette Score measures how similar a point is to its own cluster compared to other clusters. Scores near +1 mean good clustering, near 0 means overlapping clusters, and negative means wrong cluster assignment.

intermediate

What does the Davies-Bouldin Index indicate?

The Davies-Bouldin Index measures average similarity between clusters. Lower values mean clusters are compact and far apart, which is better.

intermediate

Describe 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 clusters to known true labels (e.g., Adjusted Rand Index).

intermediate

What is the Adjusted Rand Index (ARI) used for?

ARI measures similarity between the clustering result and true labels, adjusting for chance. It ranges from -1 to 1, where 1 means perfect match.

Which cluster evaluation metric ranges from -1 to 1 and measures similarity to true labels?

A Silhouette Score

B Adjusted Rand Index

C Davies-Bouldin Index

D Calinski-Harabasz Index

The Adjusted Rand Index compares clustering results to true labels and ranges from -1 to 1.

A high Silhouette Score indicates:

A Clusters overlap heavily

B Clusters are poorly formed

C Clusters are well separated and compact

D Clusters have many outliers

High Silhouette Scores mean points are closer to their own cluster than others, showing good clustering.

Which metric should be minimized for better clustering?

A Davies-Bouldin Index

B Adjusted Rand Index

C Silhouette Score

D Homogeneity Score

Lower Davies-Bouldin Index values indicate better cluster separation and compactness.

Internal cluster evaluation metrics require:

A Human expert input

B True labels of data

C External validation data

D Only data and cluster assignments

Internal metrics evaluate clusters using only the data and the clusters found, without true labels.

Which metric compares clustering results to known labels adjusting for chance grouping?

A Adjusted Rand Index

B Calinski-Harabasz Index

C Davies-Bouldin Index

D Silhouette Score

Adjusted Rand Index adjusts for chance and compares clustering to true labels.

Explain how the Silhouette Score helps evaluate clustering quality.

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

Describe the difference between internal and external cluster evaluation metrics with examples.

Consider whether true labels are needed.

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