nag mv hierar cluster analysis (g03ecc) performs hierarchical cluster analysis. 2. Specification #include <nag.h> #include <nagg03.h>

Given a distance or dissimilarity matrix for n objects (see nag mv distance mat (g03eac)), cluster analysis aims to group the n objects into a number of more or less homogeneous groups or clusters. With agglomerative clustering methods, a hierarchical tree is produced by starting with n clusters, each with a single object and then at each of n − 1 stages, merging two clusters to form a larger cluster, until all objects are in a single cluster. This process may be represented by a dendrogram (see nag mv dendrogram (g03ehc)). At each stage, the clusters that are nearest are merged, methods differ as to how the distance between the new cluster and other clusters are computed. For three clusters i, j and k let ni, nj and nk be the number of objects in each cluster and let dij, dik and djk be the distances between the clusters. Let clusters j and k be merged to give cluster jk, then the distance from cluster i to cluster jk, di.jk can be computed in the following ways. 1. Single link or nearest neighbour: di.jk =min(dij,dik). 2. Complete link or furthest neighbour: di.jk =max(dij,dik). 3. Group average: di.jk = nj nj+nk dij + nk nj+nk dik. 4. Centroid: d i.jk = nj nj+nk d ij + nk nj+nk dik − njnk (nj+nk) 2 djk