Clustering

Step 1: Understanding k-means clustering.
In the k-means algorithm, the value of k represents the number of clusters. The minimum value of k is 1, which means all data points are grouped into a single cluster. The maximum value of k is n, where each data point forms its own cluster.

Step 2: Analysis of options.
- (A) Minimum value of k=1, maximum value of k=n/2: Incorrect, the maximum number of clusters can be n, not n/2.
- (B) Minimum value of k=1, maximum value of k=n: Correct, the minimum is 1 cluster and the maximum is n clusters.
- (C) Minimum value of k=n/2, maximum value of k=n: Incorrect, the minimum value is not n/2 but 1.
- (D) Minimum value of k=2, maximum value of k=n: Incorrect, the minimum value can be 1, not 2.

Step 3: Conclusion.
The correct answer is (B) Minimum value of k=1, maximum value of k=n.

Step 1: Understanding hierarchical clustering.
In hierarchical clustering, the distance between clusters is computed using various criteria like single linkage, group average, and complete linkage. Double linkage is not a valid criterion in this context.

Step 2: Analysis of options.
- (A) Single linkage: Correct, single linkage is a valid criterion where the distance between clusters is defined as the minimum distance between elements in different clusters.
- (B) Group Average: Correct, this is a valid criterion that calculates the average distance between all points in different clusters.
- (C) Complete Linkage: Correct, this defines the distance between clusters as the maximum distance between elements in different clusters.
- (D) Double linkage: Incorrect, double linkage is not a valid criterion used in hierarchical clustering.

Step 3: Conclusion.
The correct answer is (D) Double linkage.