Finding tensor decompositions with sparse optimization

Taehyeong Kim; Jeong-Hoon Ju; Yeongrak Kim

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arXiv · 2305.13964

Finding tensor decompositions with sparse optimization

Taehyeong Kim·Jeong-Hoon Ju·Yeongrak Kim

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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 $4 \times 4$ determinant tensor as a sum of $12$ rank $1$ tensors.

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Taehyeong Kim, Jeong-Hoon Ju, Yeongrak Kim. 2023-05-23. Finding tensor decompositions with sparse optimization. https://arxiv.org/abs/2305.13964

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