In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

Question

BlackTom AI · Accepted Answer

We start by identifying the two clusters: A = {1, 2} and B = {3, 4}. In average linkage, the distance between clusters is the average of all pairwise distances between elements from each cluster.

List all cross-cluster pairs and their distances:
- D(1,3) = 2
- D(1,4) = 4
- D(2,3) = 6
- D(2,4) = 8

Next, sum these four distances: 2 + 4 + 6 + 8 = 20.

Now compute the average by dividing the total by the number of cross pairs, which is 4: 20 / 4 = 5.0.

Option-by-option check:
- a. 5.0: This matches the computed average linkage distance, since the average of {2, 4, 6, 8} is 5.0.
- b. 4.0: This would correspond to an average of a different subset or miscount, but does not equal (2 + 4 + 6 + 8)/4.
- c. 3.5: This would imply a different weighting or miscalculation of the distances; it is not the arithmetic mean of the given cross-cluster distances.
- d. 6.0: This value exceeds the actual mean of the list and would require a different aggregation rule or incorrect pairing.

In summary, the correct average linkage distance is obtained by averaging all D(i, j) with i in A and j in B, which yields 5.0, corresponding to option a.

In hierarchical clustering using average linkage, if Cluster A = {1, 2} and Cluster B = {3, 4}, and the pairwise distances are:D(1,3)=2, D(1,4)=4, D(2,3)=6, D(2,4)= 8What is the average linkage distance between clusters A and B?

View Explanation

Log in for full answers

Similar Questions