What methodology does proc varclus use to reduce the number of variables In statistics, we can use methods like principal component analysis, linear discriminant analysis for variable reduction. In SAS, there is a proc called VARCLUS which is used for variable reduction.
What methodology is it using under the hood, principal component analysis, LDA, or something else?
 A: From my SAS 9.4 documentation:

"The VARCLUS procedure divides a set of numeric variables into
  disjoint or hierarchical clusters. Associated with each cluster is a
  linear combination of the variables in the cluster. This linear
  combination can be either the first principal component (the default)
  or the centroid component (if you specify the CENTROID option). The
  first principal component is a weighted average of the variables that
  explains as much variance as possible. See Chapter 79: The PRINCOMP
  Procedure, for further details. Centroid components are unweighted
  averages of either the standardized variables (the default) or the raw
  variables (if you specify the COVARIANCE option). PROC VARCLUS tries
  to maximize the variance that is explained by the cluster components,
  summed over all the clusters. 
The cluster components are oblique, not orthogonal, even when the
  cluster components are first principal components. In an ordinary
  principal component analysis, all components are computed from the
  same variables, and the first principal component is orthogonal to the
  second principal component and to every other principal component. In
  PROC VARCLUS, each cluster component is computed from a set of
  variables that is different from all the other cluster components. The
  first principal component of one cluster might be correlated with the
  first principal component of another cluster. Hence, the PROC VARCLUS
  algorithm is a type of oblique component analysis"

