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PCPCLUSTER procedure

Forms groups of units using the densities of their PCP scores (R.W. Payne).


PRINT = string tokens What to print (cellclusters, density, summary); default summ
PLOT = string tokens What to plot (cellclusters, density, histogram, summary); default cell, dens, hist
NROOTS = scalars Numbers of dimensions to use; default 2
NPARTITIONS = scalars Numbers of partitions in each dimension; default 10
CLUSTERS = pointer Saves variates defining the clusters for each minimum number of points
CELLCLUSTERS = pointer Saves tables containing the clusters of cells for each minimum number of points
DENSITY = table Saves the table of cell densities
SUMMARY = pointer Saves the summary table
MINUNITS = variate or scalar Minimum numbers of units within cells at which to form clusters


SAVE = pointer Save structure from the PCP analysis to use; default uses the most recent analysis


The PCPCLUSTER procedure provides a way to perform cluster analysis for a large data set. The first simplification is that it reduces the number of attributes of the units by taking scores from a PCP analysis. The SAVE option supplies the save structure from the PCP analysis that is to be used. The default is to use the most recent analysis. The NROOTS parameter specifies the number of dimensions of scores to use; default 2.

The second simplification addresses the space and computing problems that occur when there are large numbers of units. Instead of forming a unit-by-unit similarity matrix, the algorithm, in the PTFCLUSTERS procedure, divides the multi-dimensional space defined by the scores into cells, and forms a density table by tabulating the number of units in each cell. The NPARTITIONS parameter specifies the number of cells to form in each dimension; default 10. The clusters are formed by finding contiguous collections of cells in which the density (or number of units) exceeds thresholds specified by the MINUNITS option. The units in these clusters of cells will be connected to each other in a similar way to the units in a hierarchical cluster analysis. Note, though, that points in sparsely populated parts of the space will not be allocated to any cluster. These units can be thus be identified as unusual or aberrant. The default for MINUNITS is to use a list of values calculated as the maximum density multiplied by 0.8, 0.75, 0.7, 0.65, 0.6, 0.55, 0.5, 0.45, 0.4, 0.35, 0.3, 0.25 and 0.2.

PTFCLUSTERS starts with the first MINUNITS value and finds a cell containing more than that number of units. This is the starting point for the first cluster. Additional cells are added to the cluster if they are neighbours of cells in the cluster containing more than that minimum number of units. When this cluster is complete, PTFCLUSTERS looks for a cell that is not in the cluster but which contains more than the minimum number of units. This provides the starting point for another cluster. The process continues until all the cells with more than that minimum number of units have been allocated to a cluster. PTFCLUSTERS then takes the next MINUNITS value and expands the clusters to contain neighbours with that smaller minimum number of units, merging clusters if they become neighbours. For each MINUNITS value, PTFCLUSTERS records the number of clusters, the mean number of units within the cells inside and outside the clusters, the mean number for units within the cells just inside and just outside the boundaries, the minimum number for units within cells on the boundaries, and the maximum number for units within cells just outside the boundaries. This summary information should help to assess which MINUNITS value gives the best set of clusters.

The PRINT option controls the printed output, with settings:

cellclusters shows how the cells are clustered for each minimum number of units,

density prints the table showing the number of units in each cell,

summary prints the summary information recorded for each minimum number of units (default).

The PLOT option specifies how the replications are plotted, with settings:

cellclusters this displays the clustering of the cells for each minimum number of points as a shade plot or as a 3-d graph if there are 2 or 3 dimensions respectively,

density displays shade plots showing the numbers of units in each pair of dimensions,

histogram plot a histogram for the numbers of units in the cells,

summary plots the summary information against the minimum numbers of units. The default is to plot all of these.

The CLUSTERS option can save a pointer containing details of the clusters of units formed at each MINUNITS value. The clusters have integer numbers, from one upwards. The pointer contains a variate for each MINUNITS value. These contain either cluster numbers, or missing values for units in cells that have not been allocated to any cluster.

The CELLCLUSTERS option can similarly save a pointer containing details of the clusters of cells formed at each MINUNITS value. The pointer contains a table for each MINUNITS value. These contain either a cluster number, or a missing value for cells that have not been allocated to any cluster.

The DENSITY option can save the table containing the number of units within each cell.

The SUMMARY option can save the summary table, in a pointer with elements labelled 'Min. no. points', 'No. clusters', 'Mean inside clusters', 'Mean outside clusters', 'Mean on boundary', 'Mean outside boundary', 'Min. on boundary' and 'Max. outside boundary'.



PCPCLUSTER calls the PTFCLUSTERS procedure to cluster the cells.

See also

Directives: CLUSTER, PCP.
Commands for: Multivariate and cluster analysis.


SPLOAD     '%data%/iris.gsh'
PCP        [PRINT=loadings,roots] !p(Sepal_Length,Sepal_Width,Petal_Length,Petal_Width);\
PEN        1,2,3; SYMBOL='circle'; CFILL='match'
DGRAPH     Scores$[*;1]; Scores$[*;2]; PEN=Species
PCPCLUSTER [PRINT=cellclusters,density,summary; PLOT=cellclusters,density,histogram,summary;\
           NROOTS=2; NPARTITIONS=8; CLUSTERS=clust]
CALCULATE  clust2 = MVREPLACE(clust[2]; 0)
GROUPS     clust2; FACTOR=Clusters
Updated on February 6, 2023

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