Joint selection of variables and clusters: recovering the underlying structure of marketing data

Clustering observations into groups is perhaps one of the more common marketing analytic techniques. Many variable-selection procedures are available for clustering, and some have exhibited good performance in simulation studies. Unfortunately, the best-performing methods often fail because they emphasize the clustering power of individual variables. For this reason, we recommend extreme caution when using the existing procedures, and we argue that enumeration of all-possible variable subsets is a preferred strategy. We also address a common decision problem-the selection of the number of clusters-and develop an index which can help guide the joint selection of variables and clusters. By way of an empirical example, we illustrate the variable-selection problem and demonstrate the use of the proposed index to jointly select variables and clusters in K-means partitioning.