Classification of multipartite states aims to obtain a set of operationally useful and finite entanglement classes under the action of either local unitary (LU) or stochastic local operation and classical communication (SLOCC). In this work, we propose a computationally simple approach to find these classes by using higher order singular value decomposition (HOSVD) and the concurrency of three lines. Since HOSVD simultaneously diagonalizes the one-body reduced density matrices (RDM) of multipartite states, the cor…