A clustering model for three-way asymmetric proximity data

This paper presents a model for clustering three-way asymmetric proximity data which represent flows or exchanges between objects observed at different occasions. In order to account for systematic differences between occasions, the asymmetric data are assumed to subsume two clustering structures common to all occasions: the first defines a standard partitioning of all objects which fits the average amount of the exchanges; the second one, which fits the imbalances, defines an “incomplete” partitioning of the objects, where some of them are allowed to remain unassigned. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is given.