K-Means clustering in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the K-Means Objective

What is the main goal of the K-Means clustering algorithm?

A To minimize the sum of squared distances between data points and their assigned cluster centers

B To find the cluster centers that maximize the total variance within clusters

C To assign each data point to a unique cluster without overlap

D To maximize the distance between all data points in the dataset

💡 Hint

Think about how K-Means groups points close to each other.

K-Means aims to find cluster centers that minimize the sum of squared distances from each point to its nearest center, creating tight groups.

❓ Predict Output

intermediate

Output of K-Means Cluster Assignments

What is the output of the following Python code snippet using scikit-learn's KMeans?

ML Python

from sklearn.cluster import KMeans
import numpy as np

X = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])
kmeans = KMeans(n_clusters=2, random_state=0).fit(X)
print(kmeans.labels_)

A [1 1 1 0 0 0]

B [0 1 0 1 0 1]

C [1 0 1 0 1 0]

D [0 0 0 1 1 1]

💡 Hint

Look at how points are grouped by proximity.

The first three points are close together and assigned to cluster 0, the last three to cluster 1.

❓ Hyperparameter

advanced

Choosing the Number of Clusters (k)

Which method is commonly used to decide the best number of clusters (k) in K-Means clustering?

A Elbow method by plotting within-cluster sum of squares versus k

B Using the highest possible k to maximize clusters

C Choosing k based on the number of features in the dataset

D Randomly selecting k without evaluation

💡 Hint

Think about a plot that shows diminishing returns.

The elbow method plots the sum of squared distances for different k values and looks for a point where improvement slows down.

❓ Metrics

advanced

Evaluating K-Means Clustering Quality

Which metric measures how well-separated the clusters are in K-Means clustering?

A Mean squared error

B Silhouette score

C Accuracy score

D Cross-entropy loss

💡 Hint

This metric ranges from -1 to 1 and considers cohesion and separation.

Silhouette score measures how similar a point is to its own cluster compared to other clusters, indicating cluster separation.

🔧 Debug

expert

Debugging K-Means Convergence Issue

You run K-Means on a dataset but notice the algorithm does not converge and runs indefinitely. Which is the most likely cause?

A The random_state parameter is not set

B The dataset contains only numerical features

C The number of clusters k is set larger than the number of unique data points

D The data is normalized before clustering

💡 Hint

Think about what happens if clusters cannot be assigned uniquely.

If k is larger than unique points, some clusters have no points, causing the algorithm to fail to update centers and not converge.

Practice

1. What does the n_clusters parameter in K-Means control?

easy

A. The initial random seed for cluster centers

B. The maximum number of iterations for the algorithm

C. The number of groups (clusters) to find in the data

D. The distance metric used to measure similarity

Solution

1. Step 1: Understand the role of n_clusters

   The n_clusters parameter tells K-Means how many groups to split the data into.

2. Step 2: Compare with other parameters

   Other parameters control iterations, distance, or randomness, but n_clusters specifically sets group count.

3. Final Answer:

   The number of groups (clusters) to find in the data -> Option C

4. Quick Check:

   n_clusters = number of groups [OK]

Hint: Remember: n_clusters means how many groups you want [OK]

Common Mistakes:

• Confusing n_clusters with max iterations
• Thinking n_clusters sets distance metric
• Assuming n_clusters controls randomness

2. Which of the following is the correct way to import KMeans from scikit-learn in Python?

easy

A. from sklearn import KMeans.cluster

B. import KMeans from sklearn.cluster

C. import sklearn.cluster.KMeans

D. from sklearn.cluster import KMeans

Solution

1. Step 1: Recall Python import syntax

   Python uses 'from module import class' to import specific classes.

2. Step 2: Match correct syntax for KMeans

   The correct import is from sklearn.cluster import KMeans.

3. Final Answer:

   from sklearn.cluster import KMeans -> Option D

4. Quick Check:

   Correct import syntax = from sklearn.cluster import KMeans [OK]

Hint: Use 'from module import class' for importing classes [OK]

Common Mistakes:

• Using wrong import order
• Trying to import with 'import' and 'from' combined incorrectly
• Using dot notation in import statement

3. Given the code below, what will be the output of print(kmeans.labels_)?

from sklearn.cluster import KMeans
import numpy as np

X = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])
kmeans = KMeans(n_clusters=2, random_state=0).fit(X)
print(kmeans.labels_)

medium

A. [0 0 0 1 1 1]

B. [1 1 1 0 0 0]

C. [0 1 0 1 0 1]

D. [1 0 1 0 1 0]

Solution

1. Step 1: Understand data grouping

   The first three points are close together near (1, y), the last three near (10, y), so KMeans will group first three as one cluster and last three as another.

2. Step 2: Check label assignment

   KMeans assigns cluster labels starting from 0. The first cluster gets label 0, second cluster label 1. But the cluster near (10, y) is assigned label 0 and near (1, y) label 1 due to initialization and fitting.

3. Final Answer:

   [1 1 1 0 0 0] -> Option B

4. Quick Check:

   Close points share label 0 or 1 [OK]

Hint: Clusters group close points; labels start at 0 [OK]

Common Mistakes:

• Assuming labels start at 1
• Mixing cluster order
• Ignoring spatial grouping

4. What is wrong with the following K-Means code snippet?

from sklearn.cluster import KMeans
X = [[1, 2], [1, 4], [1, 0]]
kmeans = KMeans(n_clusters=4)
kmeans.fit(X)
print(kmeans.labels_)

medium

A. The number of clusters (4) is greater than the number of data points (3)

B. The data X should be a numpy array, not a list

C. The KMeans class requires a random_state parameter

D. The fit method should be called with labels, not data

Solution

1. Step 1: Check cluster count vs data points

   There are only 3 data points but 4 clusters requested, which is invalid because you cannot have more clusters than points.

2. Step 2: Validate other code parts

   Using a list for X is allowed, random_state is optional, and fit expects data, not labels.

3. Final Answer:

   The number of clusters (4) is greater than the number of data points (3) -> Option A

4. Quick Check:

   Clusters ≤ data points [OK]

Hint: Clusters cannot exceed number of data points [OK]

Common Mistakes:

• Thinking data must be numpy array
• Believing random_state is mandatory
• Confusing fit input as labels

5. You have a dataset with 3 natural groups, but you run K-Means with n_clusters=5. What is the likely effect on the clustering result?

hard

A. K-Means will split some natural groups into smaller clusters, causing over-segmentation

B. K-Means will ignore extra clusters and only find 3 groups

C. K-Means will fail to run and throw an error

D. K-Means will merge groups to reduce clusters to 3 automatically

Solution

1. Step 1: Understand cluster count effect

   Setting more clusters than natural groups causes K-Means to split existing groups into smaller parts.

2. Step 2: Check K-Means behavior

   K-Means does not reduce cluster count automatically or throw error if clusters exceed natural groups; it always finds exactly n_clusters.

3. Final Answer:

   K-Means will split some natural groups into smaller clusters, causing over-segmentation -> Option A

4. Quick Check:

   More clusters than groups = splitting groups [OK]

Hint: More clusters than groups splits groups into smaller parts [OK]

Common Mistakes:

• Thinking K-Means auto-adjusts cluster count
• Expecting error when clusters > natural groups
• Assuming extra clusters are ignored