diana {cluster} | R Documentation

## DIvisive ANAlysis Clustering

### Description

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

### Usage

    diana(x, diss = inherits(x, "dist"), metric = "euclidean", stand = FALSE,
          keep.diss = n < 100, keep.data = !diss)

### 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.
`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.

### 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. See `?diana.object` for details.

### See Also

`agnes` also for background and references; `diana.object`, `daisy`, `dist`, `plot.diana`, `twins.object`.

### Examples

    data(votes.repub)
    dv <- diana(votes.repub, metric = "manhattan", stand = TRUE)
    print(dv)
    plot(dv)

    data(agriculture)
    ## Plot similar to Figure 8 in ref
    ## Not run: plot(diana(agriculture), ask = TRUE)

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