Paper ID sheet UCL-INMA-2008.074

Title

Differential-geometric Newton method for the best rank-(R1,R2,R3) approximation of tensors

Authors

Mariya Ishteva, Lieven De Lathauwer, P.-A. Absil, Sabine Van Huffel

Abstract

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-$(R_1,R_2,R_3)$ approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration [15]. This kind of algorithms are useful for many problems.

Key words

multilinear algebra; higher-order tensor; higher-order singular value decomposition; rank-(R_1,R_2,R_3) reduction; quotient manifold; differential-geometric optimization; Newton's method; Tucker compression

Status

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• Publisher's version: doi:10.1007/s11075-008-9251-2
• Preprint