Question

In k-means algorithm, if there are n data points, then what is the minimum value of k and the maximum value of k?

• A. Minimum value of k=1, maximum value of k=n/2
• B. Minimum value of k=1, maximum value of k=n
• C. Minimum value of k=n/2, maximum value of k=n
• D. Minimum value of k=2, maximum value of k=n

Hint:

In k-means clustering, the minimum value of k is 1 (one cluster), and the maximum value is n (each data point as a separate cluster).

Answer 1

The Correct Option is B

Step 1: Comprehending k-means clustering.
The k-means algorithm designates 'k' as the number of clusters. 'k' can range from 1, where all data points form a single cluster, up to 'n', where each data point constitutes its own cluster.

Step 2: Evaluating choices.
- (A) Minimum k=1, maximum k=n/2: Incorrect. The maximum number of clusters is 'n', not 'n/2'.
- (B) Minimum k=1, maximum k=n: Correct. The range is from 1 to 'n' clusters.
- (C) Minimum k=n/2, maximum k=n: Incorrect. The minimum value is 1, not 'n/2'.
- (D) Minimum k=2, maximum k=n: Incorrect. The minimum value can be 1, not 2.

Step 3: Final determination.
Option (B) is the correct answer: Minimum value of k=1, maximum value of k=n.