Iterative Methods for Symmetric Outer Product Tensor Decompositions

TL;DR

This paper introduces new iterative algorithms for symmetric outer product tensor decompositions, demonstrating faster convergence than existing methods for specific tensor types.

Contribution

The paper develops and analyzes novel iterative algorithms tailored for partially and fully symmetric tensor decompositions, improving convergence speed.

Findings

Faster convergence rates compared to standard ALS methods.

Effective algorithms for third-order partially symmetric tensors.

Efficient algorithms for fourth-order fully symmetric tensors.

Abstract

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric tensor and fourth-order fully symmetric tensor. The numerical examples indicate a faster convergence rate for the new algorithms than the standard method of alternating least squares.