Greedy Approaches to Symmetric Orthogonal Tensor Decomposition

2017/06/05 by Cun Mu, Mu, Cun, Daniel Hsu +3
Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1706.01169

openalex publication_date 2017/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Finding the symmetric and orthogonal decomposition (SOD) of a tensor is a recurring problem in signal processing, machine learning and statistics. In this paper, we review, establish and compare the perturbation bounds for two natural types of incremental rank-one approximation approaches. Numerical experiments and open questions are also presented and discussed.

Citations

• Semidefinite programming relaxations for semialgebraic problems
• The Rotation of Eigenvectors by a Perturbation. III
• Numerical optimization

Related

• Rank properties and computational methods for orthogonal tensor decompositions
• Optimal orthogonal approximations to symmetric tensors cannot always be chosen symmetric
• On the rank-one approximation of symmetric tensors
• Perturbation Bounds for (Nearly) Orthogonally Decomposable Tensors
• Decomposing tensors via rank-one approximations