Choosing K (elbow method, silhouette score) in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the Elbow Method

When using the elbow method to choose the number of clusters K in K-means clustering, what does the 'elbow' point represent?

A The point where clusters have equal sizes

B The point where adding more clusters does not significantly reduce the within-cluster sum of squares (WCSS)

C The maximum number of clusters allowed by the algorithm

D The point where the silhouette score is at its lowest value

🧠 Conceptual

intermediate

Silhouette Score Interpretation

What does a silhouette score close to 1 indicate about the clustering quality?

A Clusters are well separated and points are close to their own cluster center

B Clusters overlap heavily and points are far from their cluster center

C The number of clusters is too high

D The clustering algorithm failed to converge

❓ Predict Output

advanced

Output of Silhouette Score Calculation

What is the output of the following Python code snippet?

ML Python

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

X, _ = make_blobs(n_samples=100, centers=3, cluster_std=0.5, random_state=42)
model = KMeans(n_clusters=3, random_state=42)
labels = model.fit_predict(X)
score = silhouette_score(X, labels)
print(round(score, 2))

A 0.00

B 0.25

C 1.00

D 0.75

❓ Metrics

advanced

Choosing K Using Silhouette Scores

You run K-means clustering for K values from 2 to 6 and get these silhouette scores: {2: 0.45, 3: 0.62, 4: 0.58, 5: 0.55, 6: 0.50}. Which K should you choose based on silhouette score?

A K = 3

B K = 6

C K = 2

D K = 4

🔧 Debug

expert

Identifying the Error in Elbow Method Plot Code

What error will this code raise when trying to plot the elbow curve?

import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.datasets import make_blobs

X, _ = make_blobs(n_samples=100, centers=4, random_state=0)

wcss = []
for k in range(1, 6):
    model = KMeans(n_clusters=k)
    model.fit(X)
    wcss.append(model.inertia_)

plt.plot(range(1, 6), wcss)
plt.xlabel('Number of clusters')
plt.ylabel('WCSS')
plt.title('Elbow Method')
plt.show()

A ValueError because KMeans requires n_init parameter explicitly

B TypeError because model.inertia_ is not a float

C No error; the code runs and plots the elbow curve correctly

D NameError because matplotlib.pyplot is not imported