FINDING TENSOR DECOMPOSITIONS WITH SPARSE OPTIMIZATION

FINDING TENSOR DECOMPOSITIONS WITH SPARSE OPTIMIZATION

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.

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