85 citations · 449 across the 28 of their papers we have counts for
9 papers · 1 filter
Hadamard-Hitchcock decompositions: identifiability and computation
Alessandro Oneto, Nick Vannieuwenhoven
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decomp…
Almost all subgeneric third-order Chow decompositions are identifiable
Douglas A. Torrance, Nick Vannieuwenhoven
For real and complex homogeneous cubic polyomials in variables, we prove that the Chow variety of products of linear forms is generically complex identifiable for all ranks u…
All secant varieties of the Chow variety are nondefective for cubics and quaternary forms
Douglas A. Torrance, Nick Vannieuwenhoven
The Chow rank of a form is the length of its smallest decomposition into a sum of products of linear forms. For a generic form, this corresponds to finding the smallest secant vari…
Identifiability beyond Kruskal's bound for symmetric tensors of degree 4
Elena Angelini, Luca Chiantini, Nick Vannieuwenhoven
We show how methods of algebraic geometry can produce criteria for the identifiability of specific tensors that reach beyond the range of applicability of the celebrated Kruskal cr…
Effective criteria for specific identifiability of tensors and forms
Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven
In applications where the tensor rank decomposition arises, one often relies on its identifiability properties for interpreting the individual rank- terms appearing in the decom…
A condition number for the tensor rank decomposition
Nick Vannieuwenhoven
The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of…
Most secant varieties of tangential varieties to Veronese varieties are nondefective
Hirotachi Abo, Nick Vannieuwenhoven
We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002, which claims that the secant varieties of tangential varieties to the th Veronese embedding of the…
On generic identifiability of symmetric tensors of subgeneric rank
Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven
We prove that the general symmetric tensor in of rank r is identifiable, provided that r is smaller than the generic rank. That is, its Waring decomposition…
An algorithm for generic and low-rank specific identifiability of complex tensors
Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven
We propose a new sufficient condition for verifying whether generic rank-r complex tensors of arbitrary order admit a unique decomposition as a linear combination of rank-1 tensors…