diana { cluster } | R Documentation |
Computes a divisive hierarchical clustering of the dataset returning an object of class < code >diana code >.
diana(x, diss = inherits(x, "dist"), metric = "euclidean", stand = FALSE, stop.at.k = FALSE, keep.diss = n < 100, keep.data = !diss, trace.lev = 0)
x |
data matrix or data frame, or dissimilarity matrix or object, depending on the value of the < code >diss code > argument. In case of a matrix or data frame, each row corresponds to an observation, and each column corresponds to a variable. All variables must be numeric. Missing values (< code >NA code >s) < em >are em > allowed. In case of a dissimilarity matrix, < code >x code > is typically the output of < code >daisy code > or < code >dist code >. Also a vector of length n*(n-1)/2 is allowed (where n is the number of observations), and will be interpreted in the same way as the output of the above-mentioned functions. Missing values (NAs) are < em >not em > allowed. |
diss |
logical flag: if TRUE (default for < code >dist code > or < code >dissimilarity code > objects), then < code >x code > will be considered as a dissimilarity matrix. If FALSE, then < code >x code > will be considered as a matrix of observations by variables. |
metric |
character string specifying the metric to be used for calculating
dissimilarities between observations. |
stand |
logical; if true, the measurements in < code >x code > 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 < code >x code > is already a dissimilarity matrix, then this argument will be ignored. |
stop.at.k |
logical or integer, < code >FALSE code > by default. Otherwise must be integer, say k, in \{1,2,..,n\}, specifying that the < code >diana code > algorithm should stop early. Non-default NOT YET IMPLEMENTED. |
keep.diss, keep.data |
logicals indicating if the dissimilarities and/or input data < code >x code > should be kept in the result. Setting these to < code >FALSE code > can give much smaller results and hence even save memory allocation < em >time em >. |
trace.lev |
integer specifying a trace level for printing diagnostics during the algorithm. Default < code >0 code > does not print anything; higher values print increasingly more. |
< code >diana code > 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, < code >diana code > provides (a) the divisive coefficient (see < code >diana.object code >) which measures the amount of clustering structure found; and (b) the banner, a novel graphical display (see < code >plot.diana code >).
The < code >diana code >-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.
an object of class < code >"diana" code > representing the clustering; this class has methods for the following generic functions: < code >print code >, < code >summary code >, < code >plot code >.
Further, the class < code >"diana" code > inherits from < code >"twins" code >. Therefore, the generic function < code >pltree code > can be used on a < code >diana code > object, and < code >as.hclust code > and < code >as.dendrogram code > methods are available.
A legitimate < code >diana code > object is a list with the following components:
order |
a vector giving a permutation of the original observations to allow for plotting, in the sense that the branches of a clustering tree will not cross. |
order.lab |
a vector similar to < code >order code >, but containing observation labels instead of observation numbers. This component is only available if the original observations were labelled. |
height |
a vector with the diameters of the clusters prior to splitting. |
dc |
the divisive coefficient, measuring the clustering structure of the dataset. For each observation i, denote by d(i) the diameter of the last cluster to which it belongs (before being split off as a single observation), divided by the diameter of the whole dataset. The < code >dc code > is the average of all 1 - d(i). It can also be seen as the average width (or the percentage filled) of the banner plot. Because < code >dc code > grows with the number of observations, this measure should not be used to compare datasets of very different sizes. |
merge |
an (n-1) by 2 matrix, where n is the number of observations. Row i of < code >merge code > describes the split at step n-i of the clustering. If a number j in row r is negative, then the single observation |j| is split off at stage n-r. If j is positive, then the cluster that will be splitted at stage n-j (described by row j), is split off at stage n-r. |
diss |
an object of class < code >"dissimilarity" code >, representing the total dissimilarity matrix of the dataset. |
data |
a matrix containing the original or standardized measurements, depending on the < code >stand code > option of the function < code >agnes code >. If a dissimilarity matrix was given as input structure, then this component is not available. |
< code >agnes code > also for background and references; < code >cutree code > (and < code >as.hclust code >) for grouping extraction; < code >daisy code >, < code >dist code >, < code >plot.diana code >, < code >twins.object code >.
data(votes.repub) dv <- diana(votes.repub, metric = "manhattan", stand = TRUE) print(dv) plot(dv) ## Cut into 2 groups: dv2 <- cutree(as.hclust(dv), k = 2) table(dv2) # 8 and 42 group members rownames(votes.repub)[dv2 == 1] ## For two groups, does the metric matter ? dv0 <- diana(votes.repub, stand = TRUE) # default: Euclidean dv.2 <- cutree(as.hclust(dv0), k = 2) table(dv2 == dv.2)## identical group assignments str(as.dendrogram(dv0)) # {via as.dendrogram.twins() method} data(agriculture) ## Plot similar to Figure 8 in ref ## Not run: plot(diana(agriculture), ask = TRUE)