Clustering all three modes of three-mode data:Computational possibilities and problems

For the analysis of three-mode data sets (i.e., data sets pertaining to three different sets of entities) various component analysis techniques are available. These yield components that are summaries of the entities of each mode. Because such components are often interpreted in a more or less binary way in terms of the entities related strongest to them, it seems logical to actually constrain these components to have binary values only. In the present paper, such constrained models are proposed and algorithms for fitting these models are provided. In one of these variants, the components are constrained such that they correspond to nonoverlapping clusters of entities. Finally, a procedure is proposed for steering component values towards binary values, without actually imposing them to be binary, using penalties.