Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data

TLDR: An alternating least squares procedure is proposed, in which the individuals and the objects are partitioned into clusters, while at the same time the cluster centers are represented by unfolding.

Abstract: Classification and spatial methods can be used in conjunction to represent the individual information of similar preferences by means of groups. In the context of latent class models and using Simulated Annealing, the cluster-unfolding model for two-way two-mode preference rating data has been shown to be superior to a two-step approach of first deriving the clusters and then unfolding the classes. However, the high computational cost makes the procedure only suitable for small or medium-sized data sets, and the hypothesis of independent and normally distributed preference data may also be too restrictive in many practical situations. Therefore, an alternating least squares procedure is proposed, in which the individuals and the objects are partitioned into clusters, while at the same time the cluster centers are represented by unfolding. An enhanced Simulated Annealing algorithm in the least squares framework is also proposed in order to address the local optimum problem. Real and artificial data sets are analyzed to illustrate the performance of the model.