Three-mode partitioning

The three-mode partitioningmodel is a clusteringmodel for three-way three-mode data sets that implies a simultaneous partitioning of all three modes involved in the data. In the associated data analysis, a data array is approximated by a model array that can be represented by a three-mode partitioningmodel of a prespecified rank,minimizing a least squares loss function in terms of differences between data and model. Algorithms have been proposed for this minimization, but their performance is not yet clear. A framework for alternating least-squares methods is described in order to offset the performance problem. Furthermore, a number of both existing and novel algorithms are discussed within this framework. An extensive simulation study is reported in which these algorithms are evaluated and compared according to sensitivity to local optima. The recovery of the truth underlying the data is investigated in order to assess the optimal estimates. The ordering of the algorithms with respect to performance in finding the optimal solution appears to change as compared to the results obtained from the simulation study when a collection of four empirical data sets have been used. This finding is attributed to violations of the implicit stochastic model underlying both the least-squares loss function and the simulation study. Support for the latter attribution is found in a second simulation study. © 2006 Elsevier B.V. All rights reserved.