  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.
