In SPSS all of the few dozen Proximity (similarity measures) can be applied to variables.  (After the data are transformed and transposed)  The  Proximity matrix can then be read into the variety of cluster procedures.  Or the transposed data can be read directly into the CLUSTER, or Quick cluster procedure.  I see no reason (given that you want to cluster variables) that the TWOSTEP cluster could not read a transposed data matrix.

Of course there are all of the varieties of factor analysis which are more commonly used to group variables.  The CATPCA procedure factors categorical variables.

When the variables are used to classify or differentiate a categorical variable, there are procedures like DISCRIMINANT  or the various Procedures under CATEGORIES  or the new classification trees.

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Wolfgang M. Hartmann wrote:
Subject: Clustering Variables

a few days ago Prof. Shannon asked for references and hints
on feature selection methods. I'm also very much interested in
methods for variable clustering. I know about other predictive methods like
LARS and Lasso or SVM or the stepwise regression methods in Alan Millers
book. But, except PROC VARCLUS in SAS/STAT, which refers to Harman
and Anderberg, I do not know of any other variable cluster method.