NPTEL Learning Analytics Tools Week 7 Assignment Answers 2024

1. What is the primary goal of K-means clustering?

To maximize the distance between different clusters
To assign each point to its nearest cluster center
To minimize the distance within each cluster
To increase the number of clusters until all points are isolated

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2. Which of the following is a limitation of K-means clustering?

It is insensitive to the initial placement of cluster centers
It always finds the global optimum solution
It can only handle numerical data
It requires the number of clusters to be specified in advance

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3. In K-means clustering, how are the new cluster centers determined after assigning points to clusters?

By randomly selecting new points as cluster centers
By calculating the median of all points in each cluster
By calculating the mean of all points in each cluster
By selecting the farthest point from the current cluster center

Answer :-

4. Given the following data points: (2, 3), (3, 3), (6, 5), (8, 8), and (9, 10), if the initial cluster centers are (2, 3) and (8, 8), which of the following are the correct cluster assignments after the first iteration?

Cluster 1: (2, 3), (3, 3), (6, 5); Cluster 2: (8, 8), (9, 10)
Cluster 1: (2, 3), (3, 3); Cluster 2: (6, 5), (8, 8), (9, 10)
Cluster 1: (2, 3), (3, 3), (9, 10); Cluster 2: (6, 5), (8, 8)
Cluster 1: (2, 3), (6, 5); Cluster 2: (3, 3), (8, 8), (9, 10)

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5. You have the following data points: (1, 1), (2, 2), (4, 4), and (5, 5). If the initial cluster centers are (1, 1) and (5, 5), what will the new cluster centers be after the first iteration?

(1.5, 1.5) and (4.5, 4.5)
(2, 2) and (5, 5)
(1, 1) and (4, 4)
(1, 1) and (5.5, 5.5)

Answer :-

6. You have 6 data points in a 2-dimensional space: (1, 2), (2, 1), (4, 5), (5, 4), (8, 9), and (9, 8). You are using K-means clustering with k=3. The initial cluster centers are (1, 2), (4, 5), and (9, 8). After the first iteration, what is the total within-cluster sum of squares (WCSS)?

20.5
17
15.5
18

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7. Which of the following statements best describes hierarchical clustering?

It divides the dataset into a predetermined number of clusters
It creates a nested sequence of clusters through a series of merges or splits
It assigns data points to the nearest cluster center iteratively
It requires the number of clusters to be specified in advance.

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8. In hierarchical clustering, what is the difference between agglomerative and divisive approaches?

Agglomerative starts with one cluster and splits it, while divisive starts with individual points and merges them
Agglomerative is a bottom-up approach, and divisive is a top-down approach
Agglomerative uses centroids, while divisive uses medoids
Agglomerative clustering requires the number of clusters in advance, while divisive does not

Answer :-

9. Given the following data points: (1, 2), (2, 3), (5, 6), (8, 8). Using single-linkage (nearest neighbor) agglomerative hierarchical clustering, what is the distance between the first two clusters that will be merged?

1.0
1.41
5.0
3.0

Answer :-

10. You are given five data points: (1, 1), (2, 1), (4, 3), (5, 4), and (9, 8). After performing agglomerative hierarchical clustering using average linkage, the first two points to be merged are (1, 1) and (2, 1). What is the new cluster center?