agnes(x, diss = inherits(x, "dist"), metric = "euclidean",
stand = FALSE, method = "average", par.method,
keep.diss = n < 100, keep.data = !diss)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
dist or
dissimilarity objects), then x is assumed to be a
dissimilarity matrix. If FALSE, then x is treated as
a matrix of observations by variables.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 varimethod == "flexible", numeric vector of
length 1, 3, or 4, see in the details section.x should be kept in the result. Setting
these to FALSE can give much smaller results and hence even save
memory allocation time."agnes" representing the clustering.
See agnes.object for 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).
The method = "flexible" allows (and requires) more details:
The Lance-Williams formula specifies how dissimilarities are
computed when clusters are agglomerated (equation (32) in K.&R.,
p.237). If clusters $C_1$ and $C_2$ are agglomerated into a
new cluster, the dissimilarity between their union and another
cluster $Q$ is given by
$$D(C_1 \cup C_2, Q) = \alpha_1 * D(C_1, Q) + \alpha_2 * D(C_2, Q) +
\beta * D(C_1,C_2) + \gamma * |D(C_1, Q) - D(C_2, Q)|,$$
where the four coefficients $(\alpha_1, \alpha_2, \beta, \gamma)$
are specified by the vector par.method:
If par.method is of length 1,
say $= \alpha$, par.method is extended to
give the
Care and expertise is probably needed when using method
= "flexible" particularly for the case when par.method is
specified of longer length than one.
The weighted average (method="weighted") is the same as
method="flexible", par.method = 0.5.
Anja Struyf, Mia Hubert & Peter J. Rousseeuw (1996):
Clustering in an Object-Oriented Environment.
Journal of Statistical Software, 1.
Struyf, A., Hubert, M. and Rousseeuw, P.J. (1997). Integrating Robust Clustering Techniques in S-PLUS, Computational Statistics and Data Analysis, 26, 17--37.
agnes.object, daisy, diana,
dist, hclust, plot.agnes,
twins.object.data(votes.repub)
agn1 <- agnes(votes.repub, metric = "manhattan", stand = TRUE)
agn1
plot(agn1)
op <- par(mfrow=c(2,2))
agn2 <- agnes(daisy(votes.repub), diss = TRUE, method = "complete")
plot(agn2)
agnS <- agnes(votes.repub, method = "flexible", par.meth = 0.6)
plot(agnS)
par(op)
data(agriculture)
## Plot similar to Figure 7 in ref
plot(agnes(agriculture), ask = TRUE)
<testonly>plot(agnes(agriculture))</testonly>Run the code above in your browser using DataLab