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 ranks 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.
Angelini, E., Chiantini, L., Mazzon, A. (2019). Identifiability for a class of symmetric tensors. MEDITERRANEAN JOURNAL OF MATHEMATICS, 16(4) [10.1007/s00009-019-1363-5].
Identifiability for a class of symmetric tensors
Angelini E.;Chiantini L.;MAZZON, ANDREA
2019-01-01
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 ranks 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.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1078530