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Finding tensor decompositions with sparse optimization

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arxiv 2305.13964 v1 pith:SHFHYDTH submitted 2023-05-23 math.AC cs.NAmath.NA

Taehyeong Kim , Jeong-Hoon Ju , Yeongrak Kim This is my paper
classification math.ACcs.NAmath.NA
keywords decompositionsfindtensortensorsdeterminantoptimizationproblemrank
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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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