Trace maximization algorithm for the approximate tensor diagonalization

TL;DR

This paper introduces a Jacobi-type algorithm for approximate tensor diagonalization based on tensor trace maximization, applicable to both general and symmetric tensors, with proven convergence to stationary points.

Contribution

It develops a novel iterative algorithm for tensor diagonalization that preserves structure in symmetric cases and guarantees convergence.

Findings

Algorithm converges to stationary points

Applicable to tensors of order d≥3

Structure-preserving variant for symmetric tensors

Abstract

In this paper we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order $d\geq3$ via tensor trace maximization. For a general tensor this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand, for symmetric tensors we discuss a structure-preserving variant of this algorithm where in each iteration the same rotation is applied in all modes. We show that both versions of the algorithm converge to the stationary points of the corresponding objective functions.