# diana

##### DIvisive ANAlysis Clustering

Computes a divisive hierarchical clustering of the dataset
returning an object of class `diana`

.

- Keywords
- cluster

##### Usage

```
diana(x, diss = inherits(x, "dist"), metric = "euclidean", stand = FALSE,
stop.at.k = FALSE,
keep.diss = n < 100, keep.data = !diss, trace.lev = 0)
```

##### Arguments

- x
data matrix or data frame, or dissimilarity matrix or object, depending on the value of the

`diss`

argument.In case of a matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (

`NA`

s)*are*allowed.In case of a dissimilarity matrix,

`x`

is typically the output of`daisy`

or`dist`

. Also a vector of length n*(n-1)/2 is allowed (where n is the number of observations), and will be interpreted in the same way as the output of the above-mentioned functions. Missing values (NAs) are*not*allowed.- diss
logical flag: if TRUE (default for

`dist`

or`dissimilarity`

objects), then`x`

will be considered as a dissimilarity matrix. If FALSE, then`x`

will be considered as a matrix of observations by variables.- metric
character string specifying the metric to be used for calculating dissimilarities between observations. The currently available options are "euclidean" and "manhattan". Euclidean distances are root sum-of-squares of differences, and manhattan distances are the sum of absolute differences. If

`x`

is already a dissimilarity matrix, then this argument will be ignored.- stand
logical; if true, the measurements in

`x`

are standardized before calculating the dissimilarities. Measurements are standardized for each variable (column), by subtracting the variable's mean value and dividing by the variable's mean absolute deviation. If`x`

is already a dissimilarity matrix, then this argument will be ignored.- stop.at.k
logical or integer,

`FALSE`

by default. Otherwise must be integer, say \(k\), in \(\{1,2,..,n\}\), specifying that the`diana`

algorithm should stop early. Non-default NOT YET IMPLEMENTED.- keep.diss, keep.data
logicals indicating if the dissimilarities and/or input data

`x`

should be kept in the result. Setting these to`FALSE`

can give much smaller results and hence even save memory allocation*time*.- trace.lev
integer specifying a trace level for printing diagnostics during the algorithm. Default

`0`

does not print anything; higher values print increasingly more.

##### Details

`diana`

is fully described in chapter 6 of Kaufman and Rousseeuw (1990).
It is probably unique in computing a divisive hierarchy, whereas most
other software for hierarchical clustering is agglomerative.
Moreover, `diana`

provides (a) the divisive coefficient
(see `diana.object`

) which measures the amount of clustering structure
found; and (b) the banner, a novel graphical display
(see `plot.diana`

).

The `diana`

-algorithm constructs a hierarchy of clusterings,
starting with one large
cluster containing all n observations. Clusters are divided until each cluster
contains only a single observation.
At each stage, the cluster with the largest diameter is selected.
(The diameter of a cluster is the largest dissimilarity between any
two of its observations.)
To divide the selected cluster, the algorithm first looks for its most
disparate observation (i.e., which has the largest average dissimilarity to the
other observations of the selected cluster). This observation initiates the
"splinter group". In subsequent steps, the algorithm reassigns observations
that are closer to the "splinter group" than to the "old party". The result
is a division of the selected cluster into two new clusters.

##### Value

an object of class `"diana"`

representing the clustering;
this class has methods for the following generic functions:
`print`

, `summary`

, `plot`

.

Further, the class `"diana"`

inherits from
`"twins"`

. Therefore, the generic function `pltree`

can be
used on a `diana`

object, and `as.hclust`

and
`as.dendrogram`

methods are available.

A legitimate `diana`

object is a list with the following components:

a vector giving a permutation of the original observations to allow for plotting, in the sense that the branches of a clustering tree will not cross.

a vector similar to `order`

, but containing observation labels
instead of observation numbers. This component is only available if
the original observations were labelled.

a vector with the diameters of the clusters prior to splitting.

the divisive coefficient, measuring the clustering structure of the
dataset. For each observation i, denote by \(d(i)\) the diameter of the
last cluster to which it belongs (before being split off as a single
observation), divided by the diameter of the whole dataset. The
`dc`

is the average of all \(1 - d(i)\). It can also be seen
as the average width (or the percentage filled) of the banner plot.
Because `dc`

grows with the number of observations, this
measure should not be used to compare datasets of very different
sizes.

an (n-1) by 2 matrix, where n is the number of
observations. Row i of `merge`

describes the split at step n-i of
the clustering. If a number \(j\) in row r is negative, then the single
observation \(|j|\) is split off at stage n-r. If j is positive, then the
cluster that will be splitted at stage n-j (described by row j), is
split off at stage n-r.

an object of class `"dissimilarity"`

, representing the total
dissimilarity matrix of the dataset.

a matrix containing the original or standardized measurements, depending
on the `stand`

option of the function `agnes`

. If a
dissimilarity matrix was given as input structure, then this component
is not available.

##### See Also

`agnes`

also for background and references;
`cutree`

(and `as.hclust`

) for grouping
extraction; `daisy`

, `dist`

,
`plot.diana`

, `twins.object`

.

##### Examples

```
# NOT RUN {
data(votes.repub)
dv <- diana(votes.repub, metric = "manhattan", stand = TRUE)
print(dv)
plot(dv)
## Cut into 2 groups:
dv2 <- cutree(as.hclust(dv), k = 2)
table(dv2) # 8 and 42 group members
rownames(votes.repub)[dv2 == 1]
## For two groups, does the metric matter ?
dv0 <- diana(votes.repub, stand = TRUE) # default: Euclidean
dv.2 <- cutree(as.hclust(dv0), k = 2)
table(dv2 == dv.2)## identical group assignments
str(as.dendrogram(dv0)) # {via as.dendrogram.twins() method}
data(agriculture)
## Plot similar to Figure 8 in ref
# }
# NOT RUN {
plot(diana(agriculture), ask = TRUE)
# }
```

*Documentation reproduced from package cluster, version 2.0.7-1, License: GPL (>= 2)*