Cluster evaluation metrics in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of silhouette_score for simple clusters

What is the output of the following code that calculates the silhouette score for two simple clusters?

SciPy

from sklearn.metrics import silhouette_score
from sklearn.datasets import make_blobs

X, labels = make_blobs(n_samples=10, centers=2, cluster_std=0.5, random_state=42)
score = silhouette_score(X, labels)
print(round(score, 2))

A 0.71

B 0.15

C 1.00

D -0.50

💡 Hint

Silhouette score ranges from -1 to 1, higher means better cluster separation.

The silhouette score measures how well samples are clustered. For well-separated clusters, the score is close to 1. Here, the score is about 0.71 indicating good separation.

❓ data_output

intermediate

Number of clusters from DBSCAN labels

Given the following DBSCAN clustering labels, how many clusters (excluding noise) are detected?

SciPy

import numpy as np
labels = np.array([0, 0, 1, 1, -1, 2, 2, -1, 2])
num_clusters = len(set(labels)) - (1 if -1 in labels else 0)
print(num_clusters)

A 3

B 2

C 4

D 5

💡 Hint

Noise points are labeled as -1 and should not be counted as clusters.

The labels array has clusters labeled 0, 1, and 2. Noise points are -1 and excluded. So total clusters = 3.

🧠 Conceptual

advanced

Understanding Adjusted Rand Index (ARI)

Which statement correctly describes the Adjusted Rand Index (ARI) in cluster evaluation?

A ARI calculates the ratio of within-cluster variance to total variance.

B ARI measures the average distance between cluster centroids and data points.

C ARI is a metric that only works for hierarchical clustering methods.

D ARI measures similarity between two clusterings, adjusted for chance, with values from -1 to 1 where 1 means perfect match.

💡 Hint

Think about what ARI compares and its value range.

ARI compares two clusterings by counting pairs of points assigned consistently, adjusting for random chance. It ranges from -1 (bad) to 1 (perfect).

❓ visualization

advanced

Interpreting a silhouette plot

You run a silhouette plot for a clustering result with 3 clusters. Which of the following interpretations is correct if one cluster has many negative silhouette values?

A Negative silhouette values mean the clustering algorithm perfectly assigned points.

B The cluster with negative silhouette values is the most compact and well-separated cluster.

C The cluster with many negative silhouette values is poorly separated and may be overlapping with other clusters.

D Negative silhouette values indicate that the cluster has the highest density of points.

💡 Hint

Recall what negative silhouette values mean about point assignment.

Negative silhouette values mean points are closer to other clusters than their own, indicating poor separation or misclassification.

🔧 Debug

expert

Identify the error in Calinski-Harabasz score calculation

What error will the following code raise when calculating the Calinski-Harabasz score?

SciPy

from sklearn.metrics import calinski_harabasz_score
X = [[1, 2], [3, 4], [5, 6]]
labels = [0, 1]
score = calinski_harabasz_score(X, labels)
print(score)

A IndexError: list index out of range

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

C TypeError: calinski_harabasz_score() missing required positional argument

D No error, prints a float score

💡 Hint

Check if the labels list length matches the number of samples in X.

The labels list has length 2 but X has 3 samples. This mismatch causes a ValueError.

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