Some uniqueness results for PARAFAC2 |
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Authors: | Jos M F ten Berge Henk A L Kiers |
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Institution: | (1) Department of Psychology, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, The Netherlands |
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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.
The authors are obliged to Richard Harshman for stimulating this research, and to the Associate Editor and reviewers for suggesting
major improvements in the presentation. |
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Keywords: | three-way analysis stationary component analysis |
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