# Greedy Approaches to Symmetric Orthogonal Tensor Decomposition

## TL;DR

This paper reviews and compares perturbation bounds for incremental rank-one approximation methods in symmetric orthogonal tensor decomposition, highlighting their theoretical properties and practical implications.

## Contribution

It establishes and compares perturbation bounds for two natural incremental approaches to symmetric orthogonal tensor decomposition.

## Key findings

- Perturbation bounds for two incremental methods are derived and analyzed.
- Numerical experiments illustrate the theoretical results.
- Open questions for future research are discussed.

## 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.