Identifiability for a class of symmetric tensors
arXiv:1811.01865 · doi:10.1007/s00009-019-1363-5
Abstract
We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree 7, we use the analysis of the Hilbert function of a finite projective set, and the Cayley-Bacharach property, to prove that, when the Kruskal's rank of a decomposition of T are maximal (a condition which holds outside a Zariski closed set of measure 0), then the tensor T is identifiable, i.e. the decomposition is unique, even if the rank lies beyond the range of application of both the Kruskal's and the reshaped Kruskal's criteria.
References in corpus (5)
- Identifiability of parameters in latent structure models with many observed variables
- On generic identifiability of symmetric tensors of subgeneric rank
- Effective criteria for specific identifiability of tensors and forms
- Identifiability beyond Kruskal's bound for symmetric tensors of degree 4
- Waring decompositions and identifiability via Bertini and Macaulay2 software