FINDING TENSOR DECOMPOSITIONS WITH SPARSE

被引：0
|
作者：
Ju, Jeong-hoon [1 ]
Kim, Taehyeong [2 ]
Kim, Yeongrak [1 ,3 ]
机构：
[1] Pusan Natl Univ, Dept Math, Busan 46241, South Korea
[2] Kyungpook Natl Univ, Nonlinear Dynam & Math Applicat Ctr, Daegu 41566, South Korea
[3] Pusan Natl Univ, Inst Math Sci, Busan 46241, South Korea
来源：
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2025年 / 62卷 / 01期
关键词：
CP decomposition; tensor rank; LASSO; determinant; IDENTIFICATION; REPRESENTATION; DICTIONARIES; EQUATIONS;
D O I：
10.4134/JKMS.j230579
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
. 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 x 4 determinant tensor as a sum of 12 rank 1 tensors.
引用
收藏
页码：33 / 49
页数：17
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