Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 36, Issue 4, Pages 1567-1589Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140970276
Keywords
canonical polyadic decomposition; CANDECOMP/PARAFAC decomposition; INDSCAL; third-order tensor; uniqueness; algebraic geometry
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Funding
- Research Council KU Leuven [C16/15/059-nD, GOA/10/09 MaNet, CoE PFV/10/002]
- F.W.O [G.0830.14N, G.0881.14N]
- Belgian Federal Science Policy Office: IUAP P7 (DYSCO II, Dynamical systems, control and optimization)
- EU from the European Research Council under the European Union's Seventh Framework Programme (FP7)/ERC Advanced Grant: BIOTENSORS [339804]
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We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank-1 tensors (canonical polyadic decomposition (CPD)) is unique up to a permutation of rank-1 tensors. Then we consider the case when the tensor and all its rank-1 terms have symmetric frontal slices (INDSCAL). Our results complement the existing bounds for generic uniqueness of the CPD and relax the existing bounds for INDSCAL. The derivation makes use of algebraic geometry. We stress the power of the underlying concepts for proving generic properties in mathematical engineering.
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