Tucker core consistency for validation of restricted Tucker3 models

In Tucker3 analysis of three-way data array obtained from a chemical or biological system, it is sometimes possible to use a priori knowledge about the system to specify what is called a restricted Tucker3 model. Often, the restricted Tucker3 model is characterized by having some elements of the core forced to zero. As a simple example, an F-component PARAFAC model can be seen as a restricted (F, F, F) Tucker3 model in which only superdiagonal elements of the core are allowed to be nonzero. The core consistency diagnostic was previously introduced by Bro and Kiers for determining the proper number of components in PARAFAC analysis. In the current study, this diagnostic is extended to other restricted Tucker3 models to validate the appropriateness of the applied constraints. The new diagnostic is named Tucker core consistency (TuckCorCon). When the dimensionality and the pattern of the restricted core is valid, the simple core of restricted Tucker3 model and a corresponding unrestricted core will be similar and in this case the TuckCorCon will be close to maximum (100%). A simulated chemical equilibrium data set and two experimental data sets were used to evaluate the applicability of the TuckCorCon to decide about the appropriateness of dimensionality and pattern of the core nonzero elements in the restricted Tucker3 models.