Divisive clustering
Section of Hierarchical clustering and kernel density estimation, part of Statistical learning
Divisive clustering
| Type | Section |
| Taught in | Hierarchical clustering and kernel density estimation |
| Part | Statistical learning |
Agglomerative clustering fixes the small merges first, and every later merge inherits those decisions. Divisive clustering starts from the whole sample, so the first split is a decision about the large-scale partition. One standard rule selects the cluster of largest diameter, the maximum distance between two of its members, and moves aside the observation whose average distance to the other members is largest. The move continues until transferring another observation no longer increases the separation of the two sides. Categorical variables enter mainly through the choice of dissimilarity, for example Gower’s distance. If one partition is required, the dendrogram can be cut at a single height. The dendrogram itself remains the object the method was built to show: every nested partition at once.
A dendrogram is also a record of irreversible decisions: later merges cannot undo earlier ones. A horizontal cut chooses one partition from that record. Compare nearby cuts and inspect the observations around the large jumps before attaching a scientific interpretation to one level.
The fragment standardises columns, computes distances between rows, and cuts an average-linkage tree into three groups. Keeping the distances fixed while changing the linkage isolates the effect of the merge rule.
d <- dist(scale(x)) # Euclidean distances between standardised rows
hc <- hclust(d, method = "average") # or "single", "complete"
plot(hc) # the dendrogram
cutree(hc, k = 3) # cut the tree into 3 clustersUsed in
See also
Single, complete, and average linkage · Kernel density estimator · Hierarchical clustering · Agglomerative and divisive clustering · Properties of the linkages · Kernel density estimation · Choosing the bandwidth · Bias and variance in one bandwidth