Table 4 Comparison with existing component-based methods for three-way tables.

Orthogonal parafac

It imposes orthogonality constraints on one of the loading matrices, addressing the degeneration issue of the Parafac model and enhancing data interpretability. In our proposed approach, we compute disjoint components within the Parafac model, which inherently results in the calculation of orthogonal components. See^53,55,63,65

Rotated tucker

Rotations are applied either to one of the loading matrices or to the core of the Tucker model, preserving the model’s fit. However, data interpretation is not guaranteed in any instance. In contrast, our proposed approach ensures data interpretability by calculating disjoint components, albeit with a slight loss of fit. See^51,54,56

Sparse tucker and sparse parafac

In sparse methods, the aim is to identify entities that contribute the least to the components and assign zeros to the corresponding positions in the loading matrices (or even in the core, in the case of the Tucker model). However, it may happen that within a mode, a single entity is represented by more than one component, which complicates data interpretation. The disjoint technique is a specific type of sparse method where, for each mode, each entity is represented by one and only one component. See^{58,59,60,66,67}