On Generic Identifiability of 3-Tensors of Small Rank
From MaRDI portal
Publication:4902932
DOI10.1137/110829180zbMath1263.14053arXiv1103.2696OpenAlexW1970195563WikidataQ60307022 ScholiaQ60307022MaRDI QIDQ4902932
Luca Chiantini, Giorgio Ottaviani
Publication date: 18 January 2013
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1103.2696
Projective techniques in algebraic geometry (14N05) Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21)
Related Items (49)
Catalecticant intersections and confinement of decompositions of forms ⋮ On tangential weak defectiveness and identifiability of projective varieties ⋮ Identifiability for the k-secant variety of the Segre-Veronese varieties ⋮ Set evincing the ranks with respect to an embedded variety (symmetric tensor rank and tensor rank) ⋮ A very brief introduction to nonnegative tensors from the geometric viewpoint ⋮ Smoothed analysis for tensor methods in unsupervised learning ⋮ Generic Uniqueness Conditions for the Canonical Polyadic Decomposition and INDSCAL ⋮ Segre Functions in Multiprojective Spaces and Tensor Analysis ⋮ Non-minimum tensor rank Gabidulin codes ⋮ Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm ⋮ Computing the unique CANDECOMP/PARAFAC decomposition of unbalanced tensors by homotopy method ⋮ Topology of tensor ranks ⋮ Linearly dependent subsets of Segre varieties ⋮ $(L_r,L_r,1)$-Decompositions, Sparse Component Analysis, and the Blind Separation of Sums of Exponentials ⋮ Condition numbers for the tensor rank decomposition ⋮ Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science ⋮ Effective Criteria for Specific Identifiability of Tensors and Forms ⋮ Grassmann secants, identifiability, and linear systems of tensors ⋮ Decomposition Algorithms for Tensors and Polynomials ⋮ On the description of identifiable quartics ⋮ Identifiability for mixtures of centered Gaussians and sums of powers of quadratics ⋮ Embedded varieties, \(X\)-ranks and uniqueness or finiteness of the solutions ⋮ From non-defectivity to identifiability ⋮ An algorithm for the non-identifiability of rank-3 tensors ⋮ A Footnote to a Footnote to a Paper of B. Segre ⋮ The Condition Number of Join Decompositions ⋮ On generic identifiability of symmetric tensors of subgeneric rank ⋮ The average condition number of most tensor rank decomposition problems is infinite ⋮ A uniqueness result on the decompositions of a bi-homogeneous polynomial ⋮ Refined methods for the identifiability of tensors ⋮ Typical and admissible ranks over fields ⋮ Real identifiability vs. complex identifiability ⋮ Waring decompositions and identifiability via Bertini and Macaulay2 software ⋮ A new class of non-identifiable skew-symmetric tensors ⋮ On partial and generic uniqueness of block term tensor decompositions ⋮ Unnamed Item ⋮ A note on nonclosed tensor formats ⋮ Numerical tensor calculus ⋮ Partially symmetric tensor rank: the description of the non-uniqueness case for low rank ⋮ On identifiability of higher order block term tensor decompositions of rank Lr⊗ rank-1 ⋮ On the Terracini locus of projective varieties ⋮ Identifiability of rank-3 tensors ⋮ Pencil-Based Algorithms for Tensor Rank Decomposition are not Stable ⋮ Fiber Sampling Approach to Canonical Polyadic Decomposition and Application to Tensor Completion ⋮ Semialgebraic Geometry of Nonnegative Tensor Rank ⋮ All secant varieties of the Chow variety are nondefective for cubics and quaternary forms ⋮ Almost all subgeneric third-order Chow decompositions are identifiable ⋮ The Hitchhiker guide to: secant varieties and tensor decomposition ⋮ Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank-$(L_r,n,L_r,n,1)$ Terms---Part I: Uniqueness
Uses Software
This page was built for publication: On Generic Identifiability of 3-Tensors of Small Rank