1. Home
  2. CLUSTER directive

CLUSTER directive

Forms a non-hierarchical classification.


PRINT = string tokens Printed output required (criterion, optimum, units, typical, initial, random); default * i.e. no printing
DATA = matrix or pointer Data from which the classification is formed, supplied as a units-by-variates matrix or as a pointer containing the variates of the data matrix
CRITERION = string token Criterion for clustering (sums, predictive, within, Mahalanobis); default sums
INTERCHANGE = string token Permitted moves between groups (transfer, swop); default tran (implies swop also)
START = factor Initial classification; default * splits the units, in order, into NGROUPS classes of nearly equal size
NSTARTS = scalar Number of random starting configurations to be used; default 0
SEED = scalar Seed for the random numbers used to form random starting configurations; default 0


NGROUPS = scalars Numbers of classes into which the units are to be classified: note, the values of the scalars must be in descending order
GROUPS = factors Saves the classification formed for each number of classes
CRITERIONVALUE = scalars Saves the criterion values (representing within-class homogeneity)
BCRITERIONVALUE = scalars Saves the subsidiary criterion values (representing between-class heterogeneity for maximal predictive classification)
MEANS = matrices Saves the variate means for the groups of each classification
PREDICTORS = matrices Saves the group predictors from maximal predictive classification


Printed output is controlled by the PRINT option. This has the following possible settings.

    criterion prints the optimal criterion value.
    optimum prints the optimal classification.
    units prints the data with the units ordered into the optimal classes.
    typical prints a typical value for each class: for maximal predictive classification this is the class predictor; for the other methods it is the class mean.
    initial if this is set, the requested sections of output are also printed for the initial classification.
    random if this is set, the requested sections of output are also printed for the optimum configuration obtained from every random start.

The DATA option supplies the data to be classified. This specifies a single structure that must be either a matrix, with rows corresponding to the units and columns to the variables, or a pointer whose values are the identifiers of the variates in the data matrix. Internally, CLUSTER operates on a matrix, and so it will copy the variate values into a matrix if you supply a pointer as input; thus, it is more efficient to supply a matrix, especially with large data sets.

The CRITERION option specifies which criterion CLUSTER is to optimize. The four available settings are:

    sums minimize the within-group sum of squares (and thus maximize the between-group sum of squares);
    predictive maximal predictive classification;
    within minimize the determinant of the pooled within-class dispersion matrix;
    mahalanobis maximize the total Mahalanobis squared distance between the groups.

The default is sums.

The INTERCHANGE option specifies which types of interchange (transfers or swops) are to be used. The default is transfer, which is taken to imply that both transfers and swops are used, since a swop is simply two transfers. If you set INTERCHANGE=swop, only swops are used. If INTERCHANGE=* the algorithm does not attempt to improve the classification from the initial classification; you might want this, in conjunction with the PRINT=initial setting, to display the results for an existing classification which you do not wish to improve.

The START option can be used to supply a factor to define the initial classification. This might be constructed using the CLASSIFY procedure. If there are k classes, CLASSIFY finds the k units that are furthest apart in the multi-dimensional space defined by the data variates. These are then used as the nuclei for the classes, with each remaining unit being allocated to the class containing the nearest nucleus. The default splits the units, in order, into NGROUPS classes of nearly equal size.

As an alternative to the use of CLASSIFY, the NSTARTS option allows you to specify a number of random permutations of the initial classification to try. CLUSTER then saves the best classification that it finds. By default, NSTARTS=0, i.e. no randomization is done. The SEED option supplies the seed for the random numbers that are used to do the permutations. The default of zero continues the existing sequence of random numbers, if CLUSTER has already been used in the current Genstat job. If CLUSTER has not yet been used, Genstat picks a seed at random.

The first parameter, NGROUPS, specifies the number of groups, or classes, to be formed. Often you would want several classifications from a single data set, into different numbers of groups. In this case, the NGROUPS parameter should be a list of scalars, defining the numbers of groups in descending order. For the initial classification of the second classification, CLUSTER takes the optimal classification from the first number of groups, and does some reallocation of units to make a smaller number of groups. This is repeated, as often as required, to provide initial classifications for all the later analyses; hence the need to specify the numbers in descending order. Random starts are done only for the first number of groups.

The GROUPS parameter can specify a list of factors to save the optimal classifications. The CRITERIONVALUE parameter can specify a list of scalars to save the criterion values for each number of groups. The subsidiary criterion values involved in maximal predictive classification can be saved (also in scalars) using the BCRITERIONVALUE parameter. The MEANS parameter can save matrices containing the means of the variates within the groups of the classifications, and the PREDICTORS parameter can save matrixes containing the group predictors from maximal predictive classifications.



Action with RESTRICT

Any restrictions, for example on the variates in a DATA pointer, are ignored.

See also

Commands for: Multivariate and cluster analysis.


" Example CLUS-1: Cluster analysis with binary data."

  The data are in a file called CLUS-1.DAT
FILEREAD [NAME='%gendir%/examples/CLUS-1.DAT'] Y[1...4]; FGROUPS=no

  Carry out the non-hierarchical clustering, printing the optimal
  criterion value, the optimal classification, a typical value 
  for each class (for maximal predictive classification this
  is the class predictor) and the data with the units ordered
  into the optimal classification.

  Save the optimal classifications formed for 5 and 2 classes 
  into factors Optimum[2] and Optimum[5] respectively.  

  For binary data, the setting of the CRITERION option is predictive;
  maximal predictive classification.
CLUSTER [PRINT=criterion,optimum,typical,units; DATA=Y;\
  CRITERION=predictive] NGROUPS=5,2; GROUPS=Optimum[5,2]

  One preliminary to comparing two classifications is to tabulate them.
  To do this, use the factors Optimum[2,5] saved from the clustering, as
  classification factors in a TABULATE command. 

  The printed table shows that the first group of the classification into 
  2 groups is formed from groups 1 and 5 of the 5-group classification;
  group 2 is formed from groups 2,3 and 4.
Updated on February 6, 2023

Was this article helpful?