Agglomerative Hierarchical clustering method works on the bottom-up approach.
In Agglomerative hierarchical method, each object creates its own clusters. The single Clusters are merged to make larger clusters and the process of merging continues until all the singular clusters are merged into one big cluster that consists of all the objects.
Divisive Hierarchical clustering method works on the top-down approach. In this method all the objects are arranged within a big singular cluster and the large cluster is continuously divided into smaller clusters until each cluster has a single object.
Hierarchical Agglomerative vs Divisive Clustering
Divisive clustering is more complex as compared to agglomerative clustering, as in case of divisive clustering we need a flat clustering method as “subroutine” to split each cluster until we have each data having its own singleton cluster.
Divisive clustering is more efficient if we do not generate a complete hierarchy all the way down to individual data leaves. Time complexity of a naive agglomerative clustering is O(n3) because we exhaustively scan the N x N matrix dist_mat for the lowest distance in each of N-1 iterations. Using priority queue data structure we can reduce this complexity to O(n2logn). By using some more optimizations it can be brought down to O(n2). Whereas for divisive clustering given a fixed number of top levels, using an efficient flat algorithm like K-Means, divisive algorithms are linear in the number of patterns and clusters.
Divisive algorithm is also more accurate. Agglomerative clustering makes decisions by considering the local patterns or neighbor points without initially taking into account the global distribution of data. These early decisions cannot be undone. whereas divisive clustering takes into consideration the global distribution of data when making top-level partitioning decisions.