Cluster evaluation metrics in ML Python - Model Pipeline Trace

Model Pipeline - Cluster evaluation metrics

This pipeline shows how clustering groups data points and how we measure the quality of these groups using cluster evaluation metrics.

Data Flow - 5 Stages

1Data in

500 rows x 4 columns→Raw dataset with features→500 rows x 4 columns

[5.1, 3.5, 1.4, 0.2]

↓

2Preprocessing

500 rows x 4 columns→Scaling features to range 0-1→500 rows x 4 columns

[0.22, 0.58, 0.15, 0.10]

↓

3Feature Engineering

500 rows x 4 columns→No new features added, data ready for clustering→500 rows x 4 columns

[0.22, 0.58, 0.15, 0.10]

↓

4Model Trains

500 rows x 4 columns→K-Means clustering with k=3→500 rows x 1 cluster label

[0, 2, 1, 0, 2]

↓

5Metrics Compute

500 rows x 4 columns and 500 rows x 1 cluster label→Calculate Silhouette Score, Davies-Bouldin Index, and Calinski-Harabasz Index→3 scalar metric values

Silhouette Score=0.55, Davies-Bouldin=0.75, Calinski-Harabasz=320.4

Training Trace - Epoch by Epoch

N/A

Epoch	Loss ↓	Accuracy ↑	Observation
1	N/A	N/A	Clustering is unsupervised; no loss or accuracy. Initial cluster centers chosen.

Prediction Trace - 4 Layers

Layer 1: Input sample

Layer 2: Distance calculation

Layer 3: Assign cluster label

Layer 4: Silhouette score calculation

Model Quiz - 3 Questions

What does a higher Silhouette Score indicate about clusters?

A Clusters are well separated and dense

B Clusters overlap a lot

C Clusters have many outliers

D Clusters have fewer samples

Key Insight

Cluster evaluation metrics help us understand how good our groups are without needing labels. Silhouette Score, Davies-Bouldin, and Calinski-Harabasz each give a different view of cluster quality.

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