, Volume 29, Issue 3, pp 297-320

Lowdimensional Additive Overlapping Clustering

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Abstract

To reveal the structure underlying two-way two-mode object by variable data, Mirkin (1987) has proposed an additive overlapping clustering model. This model implies an overlapping clustering of the objects and a reconstruction of the data, with the reconstructed variable profile of an object being a summation of the variable profiles of the clusters it belongs to. Grasping the additive (overlapping) clustering structure of object by variable data may, however, be seriously hampered in case the data include a very large number of variables. To deal with this problem, we propose a new model that simultaneously clusters the objects in overlapping clusters and reduces the variable space; as such, the model implies that the cluster profiles and, hence, the reconstructed data profiles are constrained to lie in a lowdimensional space. An alternating least squares (ALS) algorithm to fit the new model to a given data set will be presented, along with a simulation study and an illustrative example that makes use of empirical data.

The research in this paper was partially supported by the Research Fund of KU Leuven (PDM-kort project 3 H100377, dr. Tom F. Wilderjans; GOA 2005/04, Prof. dr. Iven Van Mechelen), by the Belgian Science Policy (IAP P6/03, Prof. dr. Iven Van Mechelen), and by the Fund of Scientific Research (FWO)-Flanders (project G.0546.09, Prof. dr. I. Van Mechelen). The simulation study was conducted using high performance computational resources provided by the KU Leuven (http://ludit.kuleuven.be/hpc). Requests for reprints should be sent to Tom F. Wilderjans. The authors are obliged to Prof. dr. Peter Kuppens for kindly providing the data of Section 5 and to the anonymous reviewers for most helpful remarks on previous versions of this paper.