The FASTCLUS Procedure

specifies the maximum number of clusters permitted. If you omit the MAXCLUSTERS= option, a value of 100 is assumed.

establishes the minimum distance criterion for selecting new seeds. No observation is considered as a new seed unless its minimum distance to previous seeds exceeds the value given by the RADIUS= option. The default value is 0. If you specify the REPLACE=RANDOM option, the RADIUS= option is ignored.

specifies the number of bins used in the bin-sort algorithm for computing medians for LEAST=1. By default, PROC FASTCLUS uses from 10 to 100 bins, depending on the amount of memory available. Larger values use more memory and make each iteration somewhat slower, but they can reduce the number of iterations. Smaller values have the opposite effect. The minimum value of n is 5.

specifies a name for the variable in the OUTSEED= and OUT= data sets that indicates cluster membership. The default name for this variable is CLUSTER.

specifies a label for the variable CLUSTER in the OUTSEED= and OUT= data sets. By default this variable has no label.

specifies the convergence criterion. Any nonnegative value is permitted. The default value is 0.0001 for all values of p if LEAST=p is explicitly specified; otherwise, the default value is 0.02. Iterations stop when the maximum relative change in the cluster seeds is less than or equal to the convergence criterion and additional conditions on the homotopy parameter, if any, are satisfied (see the HP= option). The relative change in a cluster seed is the distance between the old seed and the new seed divided by a scaling factor. If you do not specify the LEAST= option, the scaling factor is the minimum distance between the initial seeds. If you specify the LEAST= option, the scaling factor is an scale estimate and is recomputed on each iteration. Specify the CONVERGE= option only if you specify a MAXITER= value greater than 1.

specifies the input data set containing observations to be clustered. If you omit the DATA= option, the most recently created SAS data set is used. The data must be coordinates, not distances, similarities, or correlations.

deletes cluster seeds to which n or fewer observations are assigned. Deletion occurs after processing for the DRIFT option is completed and after each iteration specified by the MAXITER= option. Cluster seeds are not deleted after the final assignment of observations to clusters, so in rare cases a final cluster might not have more than n members. The DELETE= option is ineffective if you specify MAXITER=0 and do not specify the DRIFT option. By default, no cluster seeds are deleted.

computes distances between the cluster means.

executes the second of the four steps described in the section Background. After initial seed selection, each observation is assigned to the cluster with the nearest seed. After an observation is processed, the seed of the cluster to which it is assigned is recalculated as the mean of the observations currently assigned to the cluster. Thus, the cluster seeds drift about rather than remaining fixed for the duration of the pass.

pertains to the homotopy parameter for LEAST=p, where 1 < p < 2. You should specify these options only if you encounter convergence problems when you use the default values.

For 1 < p < 2, PROC FASTCLUS tries to optimize a perturbed variant of the clustering criterion (Gonin and Money; 1989, pp. 5–6).

When the homotopy parameter is 0, the optimization criterion is equivalent to the clustering criterion. For a large homotopy parameter, the optimization criterion approaches the least squares criterion and is therefore easy to optimize. Beginning with a large homotopy parameter, PROC FASTCLUS gradually decreases it by a factor in the range [0.01,0.5] over the course of the iterations. When both the homotopy parameter and the convergence measure are sufficiently small, the optimization process is declared to have converged.

If the initial homotopy parameter is too large or if it is decreased too slowly, the optimization can require many iterations. If the initial homotopy parameter is too small or if it is decreased too quickly, convergence to a local optimum is likely. The following list gives details on setting the homotopy parameter.

requests imputation of missing values after the final assignment of observations to clusters. If an observation that is assigned (or would have been assigned) to a cluster has a missing value for variables used in the cluster analysis, the missing value is replaced by the corresponding value in the cluster seed to which the observation is assigned (or would have been assigned). If the observation cannot be assigned to a cluster, missing value replacement depends on whether or not the NOMISS option is specified. If NOMISS is not specified, missing values are replaced by the mean of all observations in the DATA= data set having a value for that variable. If NOMISS is specified, missing values are replace by the mean of only observations used in the analysis. (A weighted mean is used if a variable is specified in the WEIGHT statement.) For information about cluster assignment see the section OUT= Data Set. If you specify the IMPUTE option, the imputed values are not used in computing cluster statistics.

If you also request an OUT= data set, it contains the imputed values.

reads a SAS data set previously created with the FASTCLUS procedure by using the OUTSTAT= option. If you specify the INSTAT= option, no clustering iterations are performed and no output is displayed. Only cluster assignment and imputation are performed as an OUT= data set is created.

causes PROC FASTCLUS to use an iteratively reweighted least squares method instead of the modified Ekblom-Newton method. If you specify the IRLS option, you must also specify LEAST=p, where 1 < p < 2. Use the IRLS option only if you encounter convergence problems with the default method.

causes PROC FASTCLUS to optimize an criterion, where (Spath; 1985, pp. 62–63). Infinity is indicated by LEAST=MAX. The value of this clustering criterion is displayed in the iteration history.

If you do not specify the LEAST= option, PROC FASTCLUS uses the least squares () criterion. However, the default number of iterations is only 1 if you omit the LEAST= option, so the optimization of the criterion is generally not completed. If you specify the LEAST= option, the maximum number of iterations is increased to permit the optimization process a chance to converge. See the MAXITER= n option for details.

Specifying the LEAST= option also changes the default convergence criterion from 0.02 to 0.0001. See the CONVERGE= c for details.

When LEAST=2, PROC FASTCLUS tries to minimize the root mean squared difference between the data and the corresponding cluster means.

When LEAST=1, PROC FASTCLUS tries to minimize the mean absolute difference between the data and the corresponding cluster medians.

When LEAST=MAX, PROC FASTCLUS tries to minimize the maximum absolute difference between the data and the corresponding cluster midranges.

For general values of p, PROC FASTCLUS tries to minimize the pth root of the mean of the pth powers of the absolute differences between the data and the corresponding cluster seeds. Large values of p may cause floating-point underflow or overflow.

The divisor in the clustering criterion is either the number of nonmissing data used in the analysis or, if there is a WEIGHT statement, the sum of the weights corresponding to all the nonmissing data used in the analysis (that is, an observation with n nonmissing data contributes n times the observation weight to the divisor). The divisor is not adjusted for degrees of freedom.

The method for updating cluster seeds during iteration depends on the LEAST= option, as follows (Gonin and Money 1989).

LEAST=p	Algorithm for Computing Cluster Seeds
p = 1	Bin sort for median
1 < p < 2	Modified Merle-Spath if you specify IRLS;
	otherwise modified Ekblom-Newton
p = 2	Arithmetic mean
	Newton
	Midrange

During the final pass, a modified Merle-Spath step is taken to compute the cluster centers for or .

If you specify the LEAST=p option with a value other than 2, PROC FASTCLUS computes pooled scale estimates analogous to the root mean squared standard deviation but based on pth power deviations instead of squared deviations.

LEAST=p	Scale Estimate
p = 1	Mean absolute deviation
	Root mean pth-power absolute deviation
	Maximum absolute deviation

The divisors for computing the mean absolute deviation or the root mean pth-power absolute deviation are adjusted for degrees of freedom just like the divisors for computing standard deviations. This adjustment can be suppressed by the VARDEF= option.

lists all observations, giving the value of the ID variable (if any), the number of the cluster to which the observation is assigned, and the distance between the observation and the final cluster seed.

specifies the maximum number of iterations for recomputing cluster seeds. When the value of the MAXITER= option is greater than zero, PROC FASTCLUS executes the third of the four steps described in the section Background. In each iteration, each observation is assigned to the nearest seed, and the seeds are recomputed as the means of the clusters.

The default value of the MAXITER= option depends on the LEAST=p option.

LEAST=p	MAXITER=
Not specified	1
p = 1	20
	50
	20
p = 2	10
	20

creates an output data set to contain the cluster means and other statistics for each cluster. If you want to create a SAS data set in a permanent library, you must specify a two-level name. For more information about permanent libraries and SAS data sets, see SAS Programmers Guide: Essentials.

excludes observations with missing values from the analysis. However, if you also specify the IMPUTE option, observations with missing values are included in the final cluster assignments.

suppresses the display of all output. Note that this option temporarily disables the Output Delivery System (ODS). For more information, see Chapter 23, Using the Output Delivery System.

creates an output data set to contain all the original data, plus the new variables CLUSTER and DISTANCE. If you want to create a SAS data set in a permanent library, you must specify a two-level name. For more information about permanent libraries and SAS data sets, see SAS Programmers Guide: Essentials.

outputs information from the iteration history to the OUTSEED= data set, including the cluster seeds at each iteration.

is another name for the MEAN= data set, provided because the data set can contain location estimates other than means. The MEAN= option is still accepted.

creates an output data set to contain various statistics, especially those not included in the OUTSEED= data set. Unlike the OUTSEED= data set, the OUTSTAT= data set is not suitable for use as a SEED= data set in a subsequent PROC FASTCLUS step.

specifies a positive integer as a starting value for the pseudo-random number generator for use with REPLACE=RANDOM. If you do not specify the RANDOM= option, the time of day is used to initialize the pseudo-random number sequence.

specifies how seed replacement is performed, as follows:

specifies an input data set from which initial cluster seeds are to be selected. If you do not specify the SEED= option, initial seeds are selected from the DATA= data set. The SEED= data set must contain the same variables that are used in the data analysis.

suppresses the display of the initial cluster seeds, cluster means, and standard deviations.

prevents an observation from being assigned to a cluster if its distance to the nearest cluster seed exceeds the value of the STRICT= option. If you specify the STRICT option without a numeric value, you must also specify the RADIUS= option, and its value is used instead. In the OUT= data set, observations that are not assigned due to the STRICT= option are given a negative cluster number, the absolute value of which indicates the cluster with the nearest seed.

suppresses the display of the initial cluster seeds, statistics for variables, cluster means, and standard deviations.

specifies the divisor to be used in the calculation of variances and covariances. The default value is VARDEF=DF. The possible values of the VARDEF= option and associated divisors are as follows.

Value		Description		Divisor
DF		Error degrees of freedom
N		Number of observations		n
WDF		Sum of weights DF
WEIGHT | WGT		Sum of weights

In the preceding definitions, c represents the number of clusters.

suppresses the warning, displayed in the listing when there are two or more VAR variables, concerning the validity of the Approximate Expected Over-All R-Squared and the Cubic Clustering Criterion when the variables used in clustering are correlated. Note that the FASTCLUS procedure does not compute correlations; the warning is for a potential problem.