## 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

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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)

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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

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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

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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?

- (1.5, 1)
- (1, 2)
- (2, 2)
- (1, 1.5)

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