Can agglomerative clustering and divisive clustering get the same result in the end?

Question

Now, I know agglomerative is bottom-up method, whereas divisive is top-dowm method. However, I don't know what different between them in specific process. For example, do they all use proximity matrix to calculate any pairwise distance between samples? Besides, if I set all same parameter, like same linkage criteria, same aimed number of cluster...do they get totally same result in the end?

Answer 1

Agglomerative clustering and divisive clustering are clustering paradigms, not specific algorithms. In general different algorithms are going to return different dendrograms, but not necessarily. Here are two that return the same dendrogram (assuming that all distances are distinct):

1. Agglomerative clustering: repeatedly join the two clusters with the closest pair of points belonging to different clusters.

2. Divisive clustering: repeatedly split each cluster so as to maximize the distance between the closest pair of points belonging to different sides of the split.

It turns out that both of these clustering algorithms produce the minimum spanning tree.