Ignat Domanov

On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part II: Uniqueness of the Overall Decomposition

Canonical polyadic (also known as Candecomp/Parafac) decomposition (CPD) of a higher-order tensor is decomposition into a minimal number of rank-

On the uniqueness of the canonical polyadic decomposition of third-order tensors - Part I : Basic results and uniqueness of one factor matrix

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Generic Uniqueness Conditions for the Canonical Polyadic Decomposition and INDSCAL

tensors. In Part I, we gave an overview of existing results concerning uniqueness and presented new, relaxed, conditions that guarantee uniqueness of one factor matrix. In Part II we use these results for establishing overall CPD uniqueness in cases where none of the factor matrices has full column rank. We obtain uniqueness conditions involving Khatri--Rao products of compound matrices and Kruskal-type conditions. We consider both deterministic and generic uniqueness. We also discuss uniqueness of INDSCAL and other constrained polyadic decompositions.

Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank-

Canonical polyadic decomposition (CPD) of a higher-order tensor is decomposition into a minimal number of rank-

(L_{r,n},L_{r,n},1)

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Terms---Part II: Algorithms

tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee uniqueness of one factor matrix. These conditions involve Khatri--Rao products of compound matrices. We make links with existing results involving ranks and k-ranks of factor matrices. We give a shorter proof, based on properties of second compound matrices, of existing results concerning overall CPD uniqueness in the case where one factor matrix has full column rank. We develop basic material involving

Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition

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Generic Uniqueness of a Structured Matrix Factorization and Applications in Blind Source Separation

th compound matrices that will be instrumental in Part II for establishing overall CPD uniqueness in cases where none of the factor matrices has full column rank.

Exact line and plane search for tensor optimization

We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank-

On the Largest Multilinear Singular Values of Higher-Order Tensors

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