Some procedures for displaying results from three-way methods

Three-way Tucker analysis and CANDECOMP/PARAFAC are popular methods for the analysis of three-way data (data pertaining to three sets of entities). To interpret the results from these methods, one can, in addition to inspecti ng the component matrices and the core array, inspect visual representation s of the outcomes. In this paper, first an overview is given of plotting pr ocedures currently in use with three-way methods. Not all of these optimall y correspond to the actual approximation of the data furnished by the three -way method at hand. Next it is described how plotting procedures can be de signed that do correspond exactly to the low-dimensional description of the data by means of the three-way method at hand, and it is indicated to what extent these correspond to the ones currently in use. Specifically, proced ures are described for displaying either one set of entities (e.g. a set of chemical samples) in two- or three-dimensional plots, or a set of combinat ions of entities (e.g, pertaining to each object at each time point, thus p roviding 'trajectories' for each object). Furthermore, it is shown how, in these plots, the other entities can be plotted simultaneously (e.g. superim posing the variables on a plot with trajectories for objects), Both procedu res are summarized in an appendix. Copyright (C) 2000 John Wiley & Sons, Lt d.