Divisive Analysis
DESCRIPTION:
Returns a list representing a divisive hierarchical clustering of the dataset.
USAGE: 
diana(x, diss = F, metric = "euclidean", stand = F)
REQUIRED 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 numeric. Missing values (NAs) are allowed.

In case of a dissimilarity matrix, x is typically the output of daisy or dist. Also a vector with length n*(n-1)/2 is allowed (where n is the number of objects), and will be interpreted in the same way as the output of the above-mentioned functions. Missing values (NAs) are not allowed.

OPTIONAL ARGUMENTS:
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 objects. 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 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 absolute deviation. If x is already a dissimilarity matrix, then this argument will be ignored.

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

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 objects. Clusters are divided until each cluster contains only a single object. 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 objects.) To divide the selected cluster, the algorithm first looks for its most disparate object (i.e., which has the largest average dissimilarity to the other objects of the selected cluster). This object initiates the "splinter group". In subsequent steps, the algorithm reassigns objects 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.

BACKGROUND:
Cluster analysis divides a dataset into groups (clusters) of objects 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 objects. Partitioning methods like pam, clara, and fanny require that the number of clusters be given by the user.

REFERENCES:
Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
SEE ALSO:
agnes , diana.object , daisy , dist , plot.diana , pltree.diana .
EXAMPLES: 
dia1 <- diana(votes.repub, metric = "manhattan", stand = T)
print(dia1)
plot(dia1)


dia2 <- diana(daisy(votes.repub), diss = T, method = "complete")
pltree(dia2)


diana(dist(votes.repub), diss = T)