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國立臺灣大學 2025 · 考試 · 第 3 題

(5 points) Consider the following five DNA sequences:

a) ATCGTA
b) ATCGTT
c) GCATAG
d) GCATAC
e) TTAAGG

Which of the following statements is correct regarding the application of a $k$ -means clustering algorithm to these sequences ( $k = 3$ )?

(A)
The algorithm will always halt with exactly three optimal clusters regardless of the cluster size distance metric.
(B)
Using Hamming distance as the similarity measure, sequences a and b will always be in the same cluster.
(C)
The algorithm guarantees finding the globally optimal clustering solution for these sequences.
(D)
Using $k$ -mer frequency vectors ( $k = 2$ ) as features, sequence c and d will never be in the same cluster.
(E)
The time complexity of the $k$ -means algorithm for clustering these sequences is $O(n)$ , where $n$ is the number of sequences.

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