cluster (version 1.3-2)

diana: Divisive Analysis

Description

Returns a list representing a divisive hierarchical clustering of the dataset.

Usage

diana(x, diss = FALSE, metric = "euclidean", stand = FALSE)

Arguments

x

data matrix or dataframe, or dissimilarity matrix, depending on the value of the diss argument.

In case of a matrix or dataframe, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numer

diss

logical flag: if TRUE, 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 ar

stand

logical flag: if TRUE, then 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

Value

• an object of class "diana" representing the clustering. See diana.object for details.

BACKGROUND

Cluster analysis divides a dataset into groups (clusters) of observations that are similar to each other. Hierarchical methods like agnes, diana, and mona construct a hierarchy of clusterings, with the number of clusters ranging from one to the number of observations. Partitioning methods like pam, clara, and fanny require that the number of clusters be given by the user.

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.

References

Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

Struyf, A., Hubert, M. and Rousseeuw, P.J. (1997). Integrating Robust Clustering Techniques in S-PLUS, Computational Statistics and Data Analysis, 26, 17-37.

See Also

agnes, 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
plot(diana(agriculture), ask = TRUE)
<testonly>plot(diana(agriculture))</testonly>