On generic identifiability of symmetric tensors of subgeneric rank
نویسندگان
چکیده
منابع مشابه
On the generic rank of 3-tensors
We study the generic rank of 3-tensors using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers. We also discuss generic ranks over the real numbers. 2000 Mathematics Subject Classification. 14A25, 14P10, 15A69.
متن کاملSymmetric Tensors and Symmetric Tensor Rank
A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors. Any symmetric tensor can be decomposed into a linear combination of rank-1 tensors, each of them being symmet...
متن کاملComputing symmetric rank for symmetric tensors
We consider the problem of determining the symmetric tensor rank for symmetric tensors with an algebraic geometry approach. We give algorithms for computing the symmetric rank for 2 × · · · × 2 tensors and for tensors of small border rank. From a geometric point of view, we describe the symmetric rank strata for some secant varieties of Veronese varieties.
متن کاملIdentifiability beyond Kruskal’s Bound for Symmetric Tensors of Degree 4
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 criterion. More specifically, we deal with the symmetric identifiability of symmetric tensors in Sym4(Cn+1), i.e., quartic hypersurfaces in a projective space Pn, that have a decomposition in 2n + 1 summands of rank 1. ...
متن کاملSuccessive Rank-One Approximations of Nearly Orthogonally Decomposable Symmetric Tensors
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6762