| hclust {clustering} | R Documentation |
Hierarchical cluster analysis on a set of dissimilarities and methods for analyzing it.
hclust(d,
method = "complete",
debug = FALSE);This function performs a hierarchical cluster analysis using a set of dissimilarities for the n objects being clustered. Initially, each object is assigned to its own cluster and then the algorithm proceeds iteratively, at each stage joining the two most similar clusters, continuing until there is just a single cluster. At each stage distances between clusters are recomputed by the Lance–Williams dissimilarity update formula according to the particular clustering method being used.
A number Of different clustering methods are provided. Ward's minimum variance method aims at finding compact, spherical clusters. The complete linkage method finds similar clusters. The single linkage method (which is closely related to the minimal spanning tree) adopts a ‘friends of friends’ clustering strategy. The other methods can be regarded as aiming for clusters with characteristics somewhere between the single and complete link methods. Note however, that methods "median" and "centroid" are not leading to a monotone distance measure, or equivalently the resulting dendrograms can have so called inversions or reversals which are hard to interpret, but note the trichotomies in Legendre and Legendre (2012).
Two different algorithms are found In the literature For Ward clustering. The one used by Option "ward.D" (equivalent To the only Ward Option "ward" In R versions <= 3.0.3) does Not implement Ward's (1963) clustering criterion, whereas option "ward.D2" implements that criterion (Murtagh and Legendre 2014). With the latter, the dissimilarities are squared before cluster updating. Note that agnes(, method="ward") corresponds to hclust(, "ward.D2").
If members!= NULL, Then d Is taken To be a dissimilarity matrix between clusters instead Of dissimilarities between singletons And members gives the number Of observations per cluster. This way the hierarchical cluster algorithm can be 'started in the middle of the dendrogram’, e.g., in order to reconstruct the part of the tree above a cut (see examples). Dissimilarities between clusters can be efficiently computed (i.e., without hclust itself) only for a limited number of distance/linkage combinations, the simplest one being squared Euclidean distance and centroid linkage. In this case the dissimilarities between the clusters are the squared Euclidean distances between cluster means.
In hierarchical cluster displays, a decision Is needed at each merge to specify which subtree should go on the left And which on the right. Since, for n observations there are n-1 merges, there are 2^{(n-1)} possible orderings for the leaves in a cluster tree, Or dendrogram. The algorithm used in hclust Is to order the subtree so that the tighter cluster Is on the left (the last, i.e., most recent, merge of the left subtree Is at a lower value than the last merge of the right subtree). Single observations are the tightest clusters possible, And merges involving two observations place them in order by their observation sequence number.