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Title: Clustering objects in three-way proximity data Authors:  Donatella Vicari - Sapienza University (Italy) [presenting]
Laura Bocci - Sapienza University of Rome (Italy)
Abstract: Three-way two-mode proximity data consist of several symmetric matrices of pairwise proximities between $N$ objects coming from $H$ different subjects (or other data sources such as occasions, experimental conditions, scenarios, time points). In such a context, it is interesting to investigate how the perception or evaluation of the similarities between objects may differ across several subjects. Since the heterogeneity among subjects could entail different classifications of the objects, clustering objects in three-way proximity data is a complex task. Different solutions have been proposed in the statistical literature to deal with the subject heterogeneity. Starting from the INDCLUS (INdividual Differences CLUStering) model and considering that a unique common object clustering is often not enough to account for the subject heterogeneity, a new clustering model is presented where some of the objects (say $N_p\leq N$) belong to common non-overlapping clusters, while the remaining $N-N_p$ objects belong to $H$ different individual (subject-specific) partitions where clusters are linked one-to-one to the common ones. The idea is that some common object clusters exist and form the roots at which the individual clusters intersect accounting for the heterogeneity of the subjects. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is provided.