The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Rima Khouja - Riemannian optimization and Veronese manifold for the Waring decomposition.
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16 July 2020
July 16, 10h30-11h30 Byron Y106 & https://meet.jit.si/aromath-seminars
Riemannian optimization and Veronese manifold for the Waring decomposition.
Rima Khouja
Abstract: The symmetric tensor rank approximation problem consists in computing the best low rank approximation of a symmetric tensor. In this talk I will present a Riemannian Newton iteration for this approximation problem. I will show how we used the Veronese manifolds to parameterize this problem as a Riemannian optimization problem, and how we exploited the properties of the apolar product to present an explicit and exact formula for the gradient vector and the Hessian matrix of the method. Moreover, I will introduce a retraction operator on the Veronese manifold by directly connected to the properties of the Hankel matrices. At the end of the talk, I will present some numerical experiments to show the numerical behavior of the new method against perturbation, to compute the best real rank-1 approximation and the spectral norm of a real symmetric tensor, and to compare with some existing state-of-the-art methods for higher rank sparse symmetric tensors.
