The geometry of rank-one tensor completion
| Autor: | Kaie Kubjas, Thomas Kahle, Mario Kummer, Zvi Rosen |
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| Přispěvatelé: | Otto von Guericke University Magdeburg, Department of Mathematics and Systems Analysis, Max Planck Institute for Mathematics in the Sciences, University of Pennsylvania, Aalto-yliopisto, Aalto University |
| Rok vydání: | 2016 |
| Předmět: |
Semialgebraic set
Rank (linear algebra) Diagonal Boundary (topology) Geometry Mathematics - Statistics Theory 010103 numerical & computational mathematics Statistics Theory (math.ST) 01 natural sciences Set (abstract data type) Mathematics - Algebraic Geometry FOS: Mathematics Tensor 0101 mathematics Algebraic number Mathematics - Optimization and Control Algebraic Geometry (math.AG) Mathematics Algebra and Number Theory Applied Mathematics 010102 general mathematics ta111 Optimization and Control (math.OC) Probability distribution Geometry and Topology |
| DOI: | 10.48550/arxiv.1605.01678 |
| Popis: | The geometry of the set of restrictions of rank-one tensors to some of their coordinates is studied. This gives insight into the problem of rank-one completion of partial tensors. Particular emphasis is put on the semialgebraic nature of the problem, which arises for real tensors with constraints on the parameters. The algebraic boundary of the completable region is described for tensors parametrized by probability distributions and where the number of observed entries equals the number of parameters. If the observations are on the diagonal of a tensor of format $d\times\dots\times d$, the complete semialgebraic description of the completable region is found. Comment: 24 pages, 3 figures; v2: Final version, accepted in SIAM Journal of Applied Algebra and Geometry (SIAGA) |
| Databáze: | OpenAIRE |
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