Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/candecomp

摘要: Some existing three-way factor analysis and MDS models incorporate Cattell's “Principle of Parallel Proportional Profiles”. These can—with appropriate data—empirically determine a unique best fitting axis orientation without the need for separate rotation stage, but they have not been general enough to deal with what Tucker has called “interactions” among dimensions. This article presents proof considerably more parallel profiles model which incorporates interacting The model, Xk=AADk HBDk B', does assume symmetry in data or interactions factors. A second is presented symmetrically weighted case (i.e., whereADk=BDk). generality these allows one impose successive restrictions obtain several useful special cases, including PARAFAC2 DEDICOM.