A case of extreme simplicity of the core matrix in three-mode principal components analysis

In three-mode Principal Components Analysis, the P x Q x R core matrix G can be transformed to simple structure before it is interpreted. It is well-known that, when P = QR, G can be transformed to the identity matrix, which implies that all elements become equal to values specified a priori. In the present paper it is shown that, when P = QR - 1, G can be transformed to have nearly all elements equal to values specified a priori. A closed-form solution for this transformation is offered. Theoretical and practical implications of this simple structure transformation of G are discussed.