Which rule defines the "Complete Linkage" method in Hierarchical clustering?

Question

BlackTom AI · Accepted Answer

Complete linkage defines the inter-cluster distance as the maximum pairwise distance between points in the two clusters: D_complete(A,B) = max_{x∈A, y∈B} d(x,y).

1. Relevant knowledge points and concepts
- Hierarchical agglomerative clustering repeatedly merges the two closest clusters according to a chosen linkage rule.
- Linkage rules define how to compute distance between clusters from point-to-point distances.
- Common linkages: single (minimum), complete (maximum), average (mean of all pairs), centroid (distance between cluster centroids).

2. Step-by-step reasoning
- For two clusters A and B, enumerate all pairwise distances d(x,y) for x in A and y in B.
- Complete linkage selects the largest of these distances as the cluster-to-cluster distance.
- The cluster pair with the smallest such largest-distance is merged at each agglomeration step.

3. Example calculation (all intermediate steps)
- Let A = {(0,0),(1,0)} and B = {(4,0),(5,0)} with Euclidean distance.
- Pairwise distances: d((0,0),(4,0)) = 4; d((0,0),(5,0)) = 5; d((1,0),(4,0)) = 3; d((1,0),(5,0)) = 4.
- D_complete(A,B) = max{4,5,3,4} = 5.

4. Why the correct answer is correct
- The definition “distance between two clusters is the distance between their two most distant points” exactly restates D_complete = maximum pairwise distance, which is the standard definition of complete linkage.

5. Why other options are incorrect
- “Closest points” describes single linkage (minimum pairwise distance), not complete linkage.
- “Centroids” describes centroid linkage (distance between mean vectors), not complete linkage.
- “Average of all pairs” describes average linkage (UPGMA), not complete linkage.

6. Conclusion
- Therefore the correct rule is: “The distance between two clusters is the distance between their two most distant points.” This matches the provided answer.

Which rule defines the "Complete Linkage" method in Hierarchical clustering?单项选择题

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