Let \(C_{1}\) and \(C_{2}\) be two sets of objects. Let \(D(x, y)\) be a measure of dissimilarity between two objects \(x\) and \(y\). Consider the following definitions of dissimilarity between \(C_{1}\) and \(C_{2}\).
\[\begin{aligned} \textbf{DIS-1}(C_{1}, C_{2}) &= \max_{x \in C_{1},\, y \in C_{2}} D(x, y) \\ \textbf{DIS-2}(C_{1}, C_{2}) &= \min_{x \in C_{1},\, y \in C_{2}} D(x, y) \end{aligned}\]
Which of the following statements is/are correct?
Answer
(B), (D)
Explanation
In hierarchical clustering, the linkage rule sets the distance between two clusters from the distances between their members.
- Single linkage uses the closest pair, one object from each cluster. That is the minimum of \(D(x, y)\), which is DIS-2.
- Complete linkage uses the farthest pair. That is the maximum of \(D(x, y)\), which is DIS-1.
Options A and C swap the two rules.
Answer: B, D