diana                package:cluster                R Documentation

DIvisive ANAlysis Clustering

Description:

     Computes a divisive hierarchical clustering of the dataset
     returning an object of class 'diana'.

Usage:

     diana(x, diss = inherits(x, "dist"), metric = "euclidean", stand = FALSE,
           keep.diss = n < 100, keep.data = !diss)

Arguments:

       x: data matrix or data frame, or dissimilarity matrix or object,
          depending on the value of the '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 must be numeric. Missing values ('NA's) _are_
          allowed.

          In case of a dissimilarity matrix, 'x' is typically the
          output of 'daisy' or 'dist'.  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 _not_
          allowed. 

    diss: logical flag: if TRUE (default for 'dist' or 'dissimilarity'
          objects), 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 are the sum of absolute
          differences.  If 'x' is already a dissimilarity matrix, then
          this argument will be ignored. 

   stand: logical; if true, 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.

keep.diss, keep.data: logicals indicating if the dissimilarities and/or
          input data 'x' should be kept in the result.  Setting these
          to 'FALSE' can give much smaller results and hence even save
          memory allocation _time_.

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 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.

Value:

     an object of class '"diana"' representing the clustering; this
     class has methods for the following generic functions: 'print',
     'summary', 'plot'.

     Further, the class '"diana"' inherits from '"twins"'.  Therefore,
     the generic function 'pltree' can be used on a 'diana' object, and
     an 'as.hclust' method is available.

     A legitimate 'diana' 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 'order', 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 'dc' 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 'dc' 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 'merge' 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 '"dissimilarity"', representing the total
          dissimilarity matrix of the dataset. 

    data: a matrix containing the original or standardized
          measurements, depending on the 'stand' option of the function
          'agnes'.  If a dissimilarity matrix was given as input
          structure, then this component is not available. 

See Also:

     'agnes' also for background and references; 'cutree' (and
     'as.hclust') for grouping extraction; 'daisy', 'dist',
     'plot.diana', 'twins.object'.

Examples:

     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

     data(agriculture)
     ## Plot similar to Figure 8 in ref
     ## Not run: plot(diana(agriculture), ask = TRUE)

