UNIQUENESS OF 3-MODE FACTOR MODELS WITH SPARSE CORES - THE 3X3X3 CASE

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the thr ee modes of a three-way array; the 3MFA model also uses a three-way co re array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3M FA model the components are not uniquely determined, and it seems hard to choose among all Possible solutions. A particularly interesting fe ature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and P ARAFAC that share the good properties of the 3MFA model and the PARAFA C model: They fit (almost) as well as the 3MFA model, they are relativ ely simple and they have the same uniqueness properties as the PARAFAC model.