Symmetric Tensor Decomposition by an Iterative Eigendecomposition Algorithm

TL;DR

The paper introduces STEROID, an efficient iterative eigendecomposition algorithm for symmetric tensor decomposition, applicable to tensors of any order, with demonstrated effectiveness in large-scale problems and system identification tasks.

Contribution

It presents a novel tensor embedding technique enabling STEROID to handle tensors of arbitrary order, expanding its applicability beyond power-of-two orders.

Findings

High efficiency and accuracy demonstrated in numerical examples

Effective for large-scale tensor problems

Applicable to nonlinear system and state-space identification

Abstract

We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only eigendecompositions and least-squares fitting. Originally designed for a symmetric tensor with an order being a power of two, STEROID is shown to be applicable to any order through an innovative tensor embedding technique. Numerical examples demonstrate the high efficiency and accuracy of the proposed scheme even for large scale problems. Furthermore, we show how STEROID readily solves a problem in nonlinear block-structured system identification and nonlinear state-space identification.