Mother canonical tensor model

Canonical Tensor Decompositions

The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the tensor rank. Important basic questions are raised in this short paper, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a ...

Analysis and Approximation of the Canonical Polyadic Tensor Decomposition

We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into a projection framework and into a Rayleigh quotient. An analysis of this functional leads to several conclusions: new sufficient conditions for the existenc...

Tensor product multiplicities, canonical bases and totally positive varieties

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one tensors. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternat...

Pascal—Lab. I3S R-PC-2004-06 Canonical Tensor Decompositions

The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the tensor rank. Important basic questions are raised in this short paper, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a ...