Uni-mode and Partial Uniqueness Conditions for CANDECOMP/PARAFAC of Three-Way Arrays with Linearly Dependent Loadings

@article{Guo2012UnimodeAP,
  title={Uni-mode and Partial Uniqueness Conditions for CANDECOMP/PARAFAC of Three-Way Arrays with Linearly Dependent Loadings},
  author={Xijing Guo and Sebastian Miron and David Brie and Alwin Stegeman},
  journal={SIAM J. Matrix Analysis Applications},
  year={2012},
  volume={33},
  pages={111-129}
}
In this paper, three sufficient conditions are derived for the three-way CANDECOMP/PARAFAC (CP) model, which ensure uniqueness in one of the three modes (“uni-modeuniqueness”). Based on these conditions, a partial uniqueness condition is proposed which allows collinear loadings in only one mode. We prove that if there is uniqueness in one mode, then the initial CP model can be uniquely decomposed in a sum of lower-rank tensors for which identifiability can be independently assessed. This… CONTINUE READING
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