Schmidt decomposition is the Singular value decomposition of the coefficient matrix produced from a bipartite state that tells whether the bipartite state is an entangled state or just a direct product state.
The higher order singular value decomposition or multi-linear singular value decomposition can be thought of as a generalization of the Schmidt Decomposition.
See: Lieven De Lathauwer; Bart De Moor; Joos Vandewalle (April 2000). "A multilinear Singular Value Decomposition". SIAM Journal on Matrix Analysis. 21 (4): 1253–1278.