Question

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 \( C_2 \): \[ \text{DIS-1}(C_1, C_2) = \max_{x \in C_1, y \in C_2} D(x, y) \] \[ \text{DIS-2}(C_1, C_2) = \min_{x \in C_1, y \in C_2} D(x, y) \] Which of the following statements is/are correct?

• A. Single Linkage Clustering uses DIS-1
• B. Single Linkage Clustering uses DIS-2
• C. Complete Linkage Clustering uses DIS-2
• D. Complete Linkage Clustering uses DIS-1

Hint:

- Single Linkage uses the minimum dissimilarity between clusters (DIS-2). - Complete Linkage uses the maximum dissimilarity between clusters (DIS-1).

Answer 1

The Correct Option is B, D

We are given the definitions of DIS-1 and DIS-2. Let's analyze each option:

Option (A): "Single Linkage Clustering uses DIS-1" is incorrect. Single Linkage uses DIS-2, not DIS-1.
Option (B): "Single Linkage Clustering uses DIS-2" is correct. Single Linkage uses the minimum dissimilarity between clusters, which is DIS-2.
Option (C): "Complete Linkage Clustering uses DIS-2" is incorrect. Complete Linkage uses DIS-1, not DIS-2.
Option (D): "Complete Linkage Clustering uses DIS-1" is correct. Complete Linkage uses the maximum dissimilarity between clusters, which is DIS-1.

Thus, the correct answers are Option (B) and Option (D).