Lab Assignment -11

 

Assignment-11- week 1 October

Learning Objective: Learn Clustering Techniques ( Unsupervised Learning)

1.K-Means Clustering

Problem Statement

A shopping mall wants to group its customers into different customer segments based on their Annual Income and Spending Score.

The following data is collected from 12 customers.

Customer	Annual Income (₹ Lakhs)	Spending Score
C1	2.0	2.0
C2	2.5	2.5
C3	3.0	2.0
C4	3.5	3.0
C5	6.0	7.0
C6	6.5	6.5
C7	7.0	7.5
C8	7.5	7.0
C9	9.0	2.0
C10	9.5	2.5
C11	10.0	2.0
C12	10.5	3.0

Tasks

1. Represent the above data using a NumPy array or Pandas DataFrame.
2. Plot the customers on a 2-D scatter plot, with:
   • Annual Income on the X-axis
   • Spending Score on the Y-axis.
3. Apply the K-Means clustering algorithm with K = 3.
4. Initialize three centroids and perform the following steps manually for at least the first two iterations:
   • Calculate the Euclidean distance between each point and each centroid.
   • Assign each point to its nearest centroid.
   • Recalculate the centroid of each cluster.
   • Repeat until the clusters become stable.
5. Implement the same K-Means clustering using KMeans from Scikit-learn.
6. Display the final:
   • Cluster assignment of every customer
   • Cluster centroids
7. Plot the final clusters and their centroids using different markers/colors.
8. Compare the manually obtained clusters with the Scikit-learn result.

Additional Tasks

9. Repeat the experiment for K = 2 and K = 4.
10. Compare the resulting clusters.
11. Calculate the inertia (within-cluster sum of squares) for K = 2, 3, 4 and 5.
12. Plot the Elbow Curve and determine a suitable value of K.
13. Find the suitable value for K using silhouette method.

2.Finding the Optimal Number of Clusters using Elbow and Silhouette Methods

Problem Statement

Generate a random two-dimensional dataset containing 100 data points and use the K-Means clustering algorithm to determine the optimal number of clusters.

The optimal value of K should be determined using both:

1. Elbow Method
2. Silhouette Analysis

Tasks

1. Generate 100 random 2-D data points using NumPy. You may use:

np.random.seed(42)
X = np.random.rand(100, 2) * 10

2. Visualize the generated data using a scatter plot.
3. Apply K-Means clustering for values of K from 2 to 10.
4. For each value of K, calculate the inertia (Within-Cluster Sum of Squares).
5. Plot:

K vs. Inertia

and identify the approximate elbow point.

6. Calculate the Silhouette Score for each value of K from 2 to 10.
7. Plot:

K vs. Silhouette Score

8. Identify the value of K having the highest Silhouette Score.
9. Compare the K obtained from:
   • Elbow Method
   • Silhouette Method
10. Select a suitable value of K based on the two methods and apply K-Means clustering using the selected K.
11. Visualize the final clusters and their centroids.

3.Experiment: Agglomerative Hierarchical Clustering and Dendrogram

Problem Statement

A shopping mall wants to group its customers based on their Annual Income and Spending Score. Unlike K-Means, the company does not know the number of clusters in advance.

Use Agglomerative Hierarchical Clustering to identify natural groups among the customers and visualize the clustering process using a dendrogram.

Sample Dataset

Customer	Annual Income (₹ Lakhs)	Spending Score
C1	2.0	2.0
C2	2.5	2.5
C3	3.0	2.0
C4	3.5	3.0
C5	6.0	7.0
C6	6.5	6.5
C7	7.0	7.5
C8	7.5	7.0
C9	9.0	2.0
C10	9.5	2.5
C11	10.0	2.0
C12	10.5	3.0

Tasks

1. Create the dataset using a Pandas DataFrame.
2. Plot the customers using a scatter plot.
3. Calculate the Euclidean distance between the data points.
4. Perform Agglomerative Hierarchical Clustering using:
   • n_clusters = 3
   • single linkage
5. Display the cluster assigned to each customer.
6. Visualize the resulting clusters using a scatter plot.
7. Construct a dendrogram .
8. Label the dendrogram with the customer IDs.
9. Draw a horizontal line on the dendrogram to identify an appropriate number of clusters.
10. Compare the clusters obtained from the dendrogram with those obtained using AgglomerativeClustering from Scikit-learn.

Additional Task

Repeat the clustering using different linkage methods:

• Single linkage
• Complete linkage
• Average linkage
• Ward linkage

Compare the resulting dendrograms and discuss how the choice of linkage method affects the clusters.

4.Implement and apply K-means clustering to the Digits dataset. Experiment with different numbers of clusters and evaluate the clustering results using metrics such as inertia and silhouette score. Analyze how the choice of K affects clustering performance.

Tasks:

● Load and preprocess the Digits dataset.
● Implement K-means clustering with various numbers of clusters.
● Evaluate clustering performance using inertia and silhouette score.
● Analyze the impact of the number of clusters on clustering quality.

5.Implement and compare hierarchical (agglomerative) and partitional (K-means) clustering algorithms on the Mall Customers dataset. Discuss the strengths and weaknesses of each method based on clustering results and evaluation metrics.

Tasks:

● Load and preprocess the Mall Customers dataset.
● Apply both hierarchical (agglomerative) and K-means clustering.
● Compare results using metrics such as inertia, silhouette score, and clustering visualization.
● Discuss the advantages and disadvantages of each clustering method.