In k-means algorithm, if there are n data points, then what is the minimum value of k and the maximum value of k?
Show Hint
- Minimum value of k=1, maximum value of k=n/2
- Minimum value of k=1, maximum value of k=n
- Minimum value of k=n/2, maximum value of k=n
- Minimum value of k=2, maximum value of k=n
The Correct Option is B
Solution and Explanation
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.
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