The FASTCLUS Procedure 
PROC FASTCLUS Statement 
You must specify the MAXCLUSTERS= option or RADIUS= option or both in the PROC FASTCLUS statement.
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.
You can specify the following options in the PROC FASTCLUS statement. Table 34.1 summarizes the options.
Option 
Description 

Specify input and output data sets 

DATA= 
specifies input data set 
INSTAT= 
specifies input SAS data set previously created by the OUTSTAT= option 
SEED= 
specifies input SAS data set for selecting initial cluster seeds 
VARDEF= 
specifies divisor for variances 
Output Data Processing 

CLUSTER= 
specifies name for cluster membership variable in OUTSEED= and OUT= data sets 
CLUSTERLABEL= 
specifies label for cluster membership variable in OUTSEED= and OUT= data sets 
OUT= 
specifies output SAS data set containing original data and cluster assignments 
OUTITER 
specifies writing to OUTSEED= data set on every iteration 
OUTSEED= or MEAN= 
specifies output SAS data set containing cluster centers 
OUTSTAT= 
specifies output SAS data set containing statistics 
Initial Clusters 

DRIFT 
permits cluster to seeds to drift during initialization 
MAXCLUSTERS= 
specifies maximum number of clusters 
RADIUS= 
specifies minimum distance for selecting new seeds 
RANDOM= 
specifies seed to initializes pseudorandom number generator 
REPLACE= 
specifies seed replacement method 
Clustering Methods 

CONVERGE= 
specifies convergence criterion 
DELETE= 
deletes cluster seeds with few observations 
LEAST= 
optimizes an criterion, where 
MAXITER= 
specifies maximum number of iterations 
STRICT 
prevents an observation from being assigned to a cluster if its distance to the nearest cluster seed is large 
Arcane Algorithmic Options 

BINS= 
specifies number of bins used for computing medians for LEAST=1 
HC= 
specifies criterion for updating the homotopy parameter 
HP= 
specifies initial value of the homotopy parameter 
IRLS 
uses an iteratively reweighted least squares method instead of the modified EkblomNewton method for 
Missing Values 

IMPUTE 
imputes missing values after final cluster assignment 
NOMISS 
excludes observations with missing values 
Control Displayed Output 

DISTANCE 
displays distances between cluster centers 
LIST 
displays cluster assignments for all observations 
NOPRINT 
suppresses displayed output 
SHORT 
suppresses display of large matrices 
SUMMARY 
suppresses display of all results except for the cluster summary 
The following list provides details on these options. The list is in alphabetical order.
specifies the number of bins used in the binsort 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 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 if LEAST= 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 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 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.
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=, where . You should specify these options only if you encounter convergence problems when you use the default values.
For , 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.
specifies the criterion for updating the homotopy parameter. The homotopy parameter is updated when the maximum relative change in the cluster seeds is less than or equal to . The default is the minimum of 0.01 and 100 times the value of the CONVERGE= option.
specifies as the initial value of the homotopy parameter. The default is 0.05 if the modified EkblomNewton method is used; otherwise, it is 0.25.
also specifies as the minimum value for the homotopy parameter, which must be reached for convergence. The default is the minimum of and 0.01 times the value of the CONVERGE= option.
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 EkblomNewton method. If you specify the IRLS option, you must also specify LEAST=, where . 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= option for details.
Specifying the LEAST= option also changes the default convergence criterion from 0.02 to 0.0001. See the CONVERGE= option 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 , PROC FASTCLUS tries to minimize the th root of the mean of the th powers of the absolute differences between the data and the corresponding cluster seeds.
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 nonmissing data contributes 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 

bin sort for median 

modified MerleSpath if you specify IRLS; 
otherwise modified EkblomNewton 


arithmetic mean 

Newton 

midrange 
During the final pass, a modified MerleSpath step is taken to compute the cluster centers for or .
If you specify the LEAST= option with a value other than 2, PROC FASTCLUS computes pooled scale estimates analogous to the root mean squared standard deviation but based on th power deviations instead of squared deviations.
LEAST=p 
Scale Estimate 

mean absolute deviation 

root mean thpower absolute deviation 

maximum absolute deviation 
The divisors for computing the mean absolute deviation or the root mean thpower 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= option.
LEAST=p 
MAXITER= 
not specified 
1 

20 

50 

20 

10 

20 
creates an output data set to contain the cluster means and other statistics for each cluster. If you want to create a permanent SAS data set, you must specify a twolevel name. See "SAS Data Files" in SAS Language Reference: Concepts for more information about permanent data sets.
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 20, Using the Output Delivery System.
creates an output data set to contain all the original data, plus the new variables CLUSTER and DISTANCE. See "SAS Data Files" in SAS Language Reference: Concepts for more information about permanent data sets.
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 pseudorandom number generator for use with REPLACE=RANDOM. If you do not specify the RANDOM= option, the time of day is used to initialize the pseudorandom number sequence.
specifies how seed replacement is performed, as follows:
requests default seed replacement as described in the section Background.
requests seed replacement only when the distance between the observation and the closest seed is greater than the minimum distance between seeds.
suppresses seed replacement.
selects a simple pseudorandom sample of complete observations as initial cluster seeds.
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 


WDF 
sum of weights DF 


WEIGHT  WGT 
sum of weights 

In the preceding definitions, represents the number of clusters.
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