hclust {mva} | R Documentation |
Performs a hierarchical cluster analysis on a set of dissimilarities.
hclust(d, method = "complete") plot.hclust(hclust.obj, labels, hang = 0.1, ...)
d |
a dissimilarity structure as produced by dist . |
method |
the agglomeration method to be used. This should
be (an unambiguous abbreviation of) one of
"ward" , "single" , "complete" ,
"average" , "mcquitty" , "median" or
"centroid" . |
hclust.obj |
an object of the type produced by hclust . |
hang |
The fraction of the plot height by which labels should hang below the rest of the plot. A negative value will cause the labels to hang down from 0. |
labels |
A character vector of labels for the leaves of the
tree. By default the row names or row numbers of the original data are
used. If labels=FALSE no labels at all are plotted. |
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 LanceWilliams 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.
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.
merge |
an n-1 by 2 matrix.
Row i of merge describes the merging of clusters
at step i of the clustering.
If an element j in the row is negative,
then observation -j was merged at this stage.
If j is positive then the merge
was with the cluster formed at the (earlier) stage j
of the algorithm.
Thus negative entries in merge indicate agglomerations
of singletons, and positive entries indicate agglomerations
of non-singletons. |
height |
a set of n-1 non-decreasing real values.
The clustering height: that is, the value of
the criterion associated with the clustering
method for the particular agglomeration. |
order |
a vector giving the permutation of the original
observations suitable for plotting, in the sense that a cluster
plot using this ordering and matrix merge will not have
crossings of the branches. |
labels |
labels for each of the objects being clustered. |
call |
the call which produced the result. |
method |
the cluster method that has been used. |
dist.method |
the distance that has been used to create d
(only returned if the distance object has a "method"
attribute). |
The hclust
function is based on Fortran code
contributed to STATLIB by F. Murtagh.
Everitt, B. (1974). Cluster Analysis. London: Heinemann Educ. Books.
Hartigan, J. A. (1975). Clustering Algorithms. New York: Wiley.
Sneath, P. H. A. and R. R. Sokal (1973). Numerical Taxonomy. San Francisco: Freeman.
Anderberg, M. R. (1973). Cluster Analysis for Applications. Academic Press: New York.
Gordon, A. D. (1981). Classification. London: Chapman and Hall.
Murtagh, F. (1985). ``Multidimensional Clustering Algorithms'', in COMPSTAT Lectures 4. Wuerzburg: Physica-Verlag (for algorithmic details of algorithms used).
library(mva) data(USArrests) hc <- hclust(dist(USArrests), "ave") plot(hc, hang=-1) plot(hc)