Finding tensor decompositions with sparse optimization

2023/05/23 by Tae-Hyeong Kim, Kim, Taehyeong, Jeong-Hoon Ju +3 · 1 citation
Computer Science · Mathematics · #Algorithms and Data Compression #Commutative Algebra (math.AC) #Computational Physics and Python Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2305.13964

openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank 1 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 4 × 4 determinant tensor as a sum of 12 rank 1 tensors.

Cited by

• The border rank of the 4 × 4 determinant tensor is twelve

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