`hclust`

.
```
hclust(d, method = "complete", members=NULL)
flashClust(d, method = "complete", members=NULL)
```

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"`

. members

`NULL`

or a vector with length size of
`d`

. See the ‘Details’ section.-
Returned value is the same as that of
- 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).

`hclust`

:
An object of class `hclust`

for details on available clustering methods. 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.

`flashClust`

is a wrapper for compatibility with older code.

This implementation is mentioned in

Peter Langfelder, Steve Horvath (2012) Fast R Functions for Robust Correlations and Hierarchical Clustering. Journal of Statistical Software, 46(11), 1-17. http://www.jstatsoft.org/v46/i11/

F.Murtagh's software web site: http://www.classification-society.org/csna/mda-sw/ , section 6

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth \& Brooks/Cole. (S version.)

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. (1999).
*Classification*. Second Edition.
London: Chapman and Hall / CRC

Murtagh, F. (1985).
“Multidimensional Clustering Algorithms”, in
*COMPSTAT Lectures 4*.
Wuerzburg: Physica-Verlag
(for algorithmic details of algorithms used).

McQuitty, L.L. (1966).
Similarity Analysis by Reciprocal Pairs for Discrete and Continuous
Data.
*Educational and Psychological Measurement*, **26**, 825--831.

`hclust`

# generate some data to cluster set.seed(1); nNodes = 2000; # Random "distance" matrix dst = matrix(runif(n = nNodes^2, min = 0, max = 1), nNodes, nNodes); # Time the flashClust clustering system.time( { h1 = hclust(as.dist(dst), method= "average"); } ); # Time the standard R clustering system.time( { h2 = stats::hclust(as.dist(dst), method = "average"); } ); all.equal(h1, h2) # What is different: h1[[6]] h2[[6]] # Everything but the 'call' component is the same; in particular, the trees are exactly equal.