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: 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.