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Psychometrika

, Volume 61, Issue 1, pp 123–132 | Cite as

Some uniqueness results for PARAFAC2

  • Jos M. F. ten Berge
  • Henk A. L. Kiers
Article

Abstract

Whereas the unique axes properties of PARAFAC1 have been examined extensively, 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 have recently shown, subject to mild assumptions, that PARAFAC2 is unique 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 matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2.

Key words

three-way analysis stationary component analysis 

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Copyright information

© The Psychometric Society 1996

Authors and Affiliations

  • Jos M. F. ten Berge
    • 1
  • Henk A. L. Kiers
    • 1
  1. 1.Department of PsychologyUniversity of GroningenGroningenThe Netherlands

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