Agglomerative Nesting
DESCRIPTION:
Returns a list representing an agglomerative hierarchical clustering of the dataset.
USAGE: 
agnes(x, diss = F, metric = "euclidean", stand = F, method = "average")
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.

method:
character string defining the clustering method. The three methods implemented are "average", "complete", and "single" linkage.

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

DETAILS:
agnes is fully described in chapter 5 of Kaufman and Rousseeuw (1990). Compared to other agglomerative clustering methods such as hclust, agnes has the following features: (a) it yields the agglomerative coefficient (see agnes.object) which measures the amount of clustering structure found; and (b) apart from the usual tree it also provides the banner, a novel graphical display (see plot.agnes).

The agnes-algorithm constructs a hierarchy of clusterings. At first, each object is a small cluster by itself. Clusters are merged until only one large cluster remains which contains all the objects. At each stage the two "nearest" clusters are combined to form one larger cluster. For method="average", the distance between two clusters is the average of the dissimilarities between the points in one cluster and the points in the other cluster. In method="single", we use the minimal dissimilarity between a point in the first cluster and a point in the second cluster. When method="complete", we use the maximal dissimilarity between a point in the first cluster and a point in the second cluster.

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.object , daisy , diana , dist , hclust , plot.agnes , pltree.agnes .
EXAMPLES: 
agn1 <- agnes(votes.repub, metric = "manhattan", stand = T)
print(agn1)
plot(agn1)


agn2 <- agnes(daisy(votes.repub), diss = T, method = "complete")
pltree(agn2)


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