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Machine learning MCQ - Hierarchical agglomerative clustering - single linkage and complete linkage

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Machine Learning MCQ - Hierarchical agglomerative clustering - single linkage and complete linkage

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1. After three iterations of Hierarchical Agglomerative Clustering using Euclidean distance between points, we get the 3 clusters: C1 = {2, 4}, C2 = {7, 8} and C3 = {12, 14}. What is the distance between clusters C1 and C2 using Single Linkage and Complete Linkage?

a) 2, 2

b) 3, 4

c) 3, 6

d) 5, 6

Answer: (c) 3, 6

 

Single linkage

In single linkage, we define the distance between two clusters as the minimum distance between any single data point in the first cluster and any single data point in the second cluster. On the basis of this definition of distance between clusters, at each stage of the process we combine the two clusters with the smallest single linkage distance.

As per single linkage, d(C1, C2) = d({2, 4}, {7, 8}) = min(|2-7|, |2-8|, |4-7|, |4-8|)

                                                                                    = min(5, 6, 3, 4) = 3

Single linkage hierarchical clustering

In single-link (or single linkage) hierarchical clustering, we merge in each step the two clusters whose two closest members have the smallest distance (or: the two clusters with the smallest minimum pairwise distance).

 

Complete linkage

In complete linkage, we define the distance between two clusters to be the maximum distance between any single data point in the first cluster and any single data point in the second cluster. On the basis of this definition of distance between clusters, at each stage of the process we combine the two clusters that have the smallest complete linkage distance.

As per complete linkage, d(C1, C2) = d({2, 4}, {7, 8}) = max(|2-7|, |2-8|, |4-7|, |4-8|)

                                                                                    = max(5, 6, 3, 4) = 6

Complete linkage hierarchical clustering

In complete-link (or complete linkage) hierarchical clustering, we merge in each step the two clusters whose merger has the smallest diameter (or: the two clusters with the smallest maximum pairwise distance).

 

 

 

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Related links:

Hierarchical agglomerative clustering

How is single link distance calculated?

How is complete linkage distance calculated?

What is single linkage method?

What is complete linkage method?

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