cluster (version 1.2-1)

agnes: 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")

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

method

character string defining the clustering method. The five methods implemented are "average" (group average method), "single" (single linkage), "complete" (complete linkage), "ward" (Ward's method), and "weighted" (weighted average linkage). Default is "

Value

• an object of class "agnes" representing the clustering. See agnes.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

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 observation is a small cluster by itself. Clusters are merged until only one large cluster remains which contains all the observations. 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 smallest dissimilarity between a point in the first cluster and a point in the second cluster (nearest neighbor method). When method="complete", we use the largest dissimilarity between a point in the first cluster and a point in the second cluster (furthest neighbor method).

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.object, daisy, diana, dist, hclust, plot.agnes, twins.object.

Examples

data(votes.repub)
agn1 <- agnes(votes.repub, metric = "manhattan", stand = TRUE)
print(agn1)
plot(agn1)
agn2 <- agnes(daisy(votes.repub), diss = TRUE, method = "complete")
plot(agn2)

data(agriculture)
## Plot similar to Figure 7 in ref
plot(agnes(agriculture), ask = TRUE)
<testonly>plot(agnes(agriculture))</testonly>