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Overview of constrained PARAFAC models

Abstract : Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first reviewed. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for N-th order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models.
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https://hal.archives-ouvertes.fr/hal-01246040
Contributor : Gérard Favier <>
Submitted on : Friday, December 18, 2015 - 12:15:43 AM
Last modification on : Thursday, March 5, 2020 - 12:20:25 PM

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Gérard Favier, André de Almeida. Overview of constrained PARAFAC models . EURASIP Journal on Advances in Signal Processing, SpringerOpen, 2014, 2014 (1), pp.1-41. ⟨10.1186/1687-6180-2014-142⟩. ⟨hal-01246040⟩

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