CPclus: Candecomp/Parafac Clustering Model for Three-Way Data

A novel clustering model, CPclus, for three-way data concerning a set of objects on which variables are measured by different subjects is proposed. The main aim of the proposal is to simultaneously summarize the objects through clusters and both variables and subjects through components. The object clusters are found by adopting a K-means-based strategy where the centroids are reduced according to the Candecomp/Parafac model in order to exploit the three-way structure of the data. The clustering process is carried out in order to reveal between-cluster differences in mean. Least-squares fitting is performed by using an iterative alternating least-squares algorithm. Model selection is addressed by considering an elbow-based method. An extensive simulation study and some real-life applications show the effectiveness of the proposal, also in comparison with its potential competitors.