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 inspecting the component matrices and the core array, inspect visual representations of the outcomes. In this paper, first an overview is given of plotting procedures currently in use with three-way methods. Not all of these optimally 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 designed 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, procedures 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 combinations of entities (e.g. pertaining to each object at each time point, thus providing ‘trajectories’ for each object). Furthermore, it is shown how, in these plots, the other entities can be plotted simultaneously (e.g. superimposing the variables on a plot with trajectories for objects). Both procedures are summarized in an appendix.