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?
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?
Show Hint
- Single Linkage uses the minimum dissimilarity between clusters (DIS-2).
- Complete Linkage uses the maximum dissimilarity between clusters (DIS-1).
Updated On: Feb 3, 2026
- Single Linkage Clustering uses DIS-1
- Single Linkage Clustering uses DIS-2
- Complete Linkage Clustering uses DIS-2
- Complete Linkage Clustering uses DIS-1
Show Solution
Verified By Collegedunia
The Correct Option is B, D
Solution and Explanation
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).
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).
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