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.