Finding tensor decompositions with sparse optimization
Commutative Algebra
2023-05-24 v1 Numerical Analysis
Numerical Analysis
Abstract
In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition problem as a sparse optimization problem. As applications, we design experiments to find some CP decompositions of the matrix multiplication and determinant tensors. In particular, we find a new formula for the determinant tensor as a sum of rank tensors.
Cite
@article{arxiv.2305.13964,
title = {Finding tensor decompositions with sparse optimization},
author = {Taehyeong Kim and Jeong-Hoon Ju and Yeongrak Kim},
journal= {arXiv preprint arXiv:2305.13964},
year = {2023}
}
Comments
19 pages, 2 figures. This paper supercedes arXiv:2303.07842