Rank-one approximation of a higher-order tensor by a Riemannian trust-region method
Authors
Jianheng Cheng, Wen Huang*
Abstract
In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on the Cartesian product of manifolds. A Riemannian trust-region method with block diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective.
Key words
Higher-order tensor; rank-one approximation; Riemannian Hessian; trust-region method
Status
Submitted
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