Symmetric Tensor Decomposition by an Iterative Eigendecomposition Algorithm

2014/09/17 by Kim Batselier, Batselier, Kim, Ngai Wong +1 · 1 citation
Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Power System Optimization and Stability #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1409.4926

openalex publication_date 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications

Cited by

• Identifiability of Deep Polynomial Neural Networks

Related

• Iterative Methods for Symmetric Outer Product Tensor Decompositions
• Subspace power method for symmetric tensor decomposition
• On the rank-one approximation of symmetric tensors
• Symmetric Orthogonal Tensor Decomposition is Trivial
• Greedy Approaches to Symmetric Orthogonal Tensor Decomposition