SOME UNIQUENESS RESULTS FOR PARAFAC2

Whereas the unique axes properties of PARAFAC1 have been examined exte nsively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy h ave recently shown, subject to mild assumptions, that PARAFAC2 is uniq ue when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal ma trices of weights are constrained to be non-negative, three matrices a re enough to have uniqueness in the rank two case of PARAFAC2.