Principal components analysis constructs components that are linear combinations of all the variables in the analysis. In contrast, the Cluster Variables option constructs components that are linear combinations of variables in a cluster of similar variables. The entire set of variables is partitioned into clusters. For each cluster, a cluster component is constructed using the first principal component of the variables in that cluster. This cluster component is the linear combination that explains as much of the variation as possible among the variables in that cluster.
You can use the Cluster Variables option as a dimension-reduction method. A substantial part of the variation in a large set of variables can often be represented by cluster components or by the most representative variable in the cluster. These new variables can then be used in predictive or other modeling techniques. The new cluster-based variables are usually more interpretable than principal components based on all the variables.
Principal components constructed from a common set of variables are orthogonal. However, cluster components are not orthogonal because they are constructed from distinct sets of variables.
When you have a large set of variables, the Cluster Variables platform uses an algorithm based on the singular value decomposition to shorten computation time. For additional background, see Wide Linear Methods and the Singular Value Decomposition in the Statistical Details section.