Non‐triviality and identification of a constrained Tucker3 analysis

Properties of estimated parameters of models of chemical systems are important. This paper focuses on two properties of such estimated parameters: triviality and uniqueness. If a chemical system is analyzed using a Tucker3 model, then the resulting core can often be rotated to a simple structure containing zeros. This means that it is possible that a prespecified pattern of zero and non‐zero elements of the core, as used in e.g. constrained Tucker3 models, is not an active constraint; that is, the zeros can be obtained trivially for free. Once a non‐trivial pattern of zeros in the core is specified, the question arises whether this pattern is sufficient for obtaining unique loadings. Both issues are discussed in this paper and it is shown that the model used by Gurden et al. ( J. Chemometrics 2001; 15: 101–121) does essentially involve a non‐trivial core and implies rotationally unique parameter estimates.