2023/09/14 by Claudio Turchetti, Turchetti, Claudio · 1 citation
Computer Science · Mathematics · #Computational Physics and Python Applications #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2309.07819
openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a low-dimensional subspace by solving an optimization problem and assuming the number of components is fixed. However, even though this algorithm is efficient and easy to implement, it often converges to poor local minima and suffers from outliers and noise. The aim of this paper is to develop a mathematical framework for exact tensor decomposition that is able to represent a tensor as the sum of a finite number of low-rank tensors. In the paper three different problems will be carried out to derive: i) the decomposition of a non-negative self-adjoint tensor operator; ii) the decomposition of a linear tensor transformation; iii) the decomposition of a generic tensor.