Nonmetric multidimensional scaling with clustering of subjects

A new nonmetric multidimensional scaling method is devised to analyze three-way data concerning inter-stimulus similarities obtained from many subjects. It is assumed that subjects are classified into a small number of clusters and that the stimulus configuration is specific to each cluster. Under this assumption, the classification of subjects and the scaling used to derive the configurations for clusters are simultaneously performed using an alternating least-squares algorithm. The monotone regression of ordinal similarity data, the scaling of stimuli and the K -means clustering of subjects are iterated in the algorithm. The method is assessed using a simulation and its practical use is illustrated with the analysis of real data. Finally, some extensions are considered.