  Approximating higher-order tensors by the Tucker format has been applied in
many fields such as psychometrics, chemometrics, signal processing, pattern
classification, and so on. In this paper, we propose some new Tucker-like
approximations based on the modal semi-tensor product (STP), especially, a new
singular value decomposition (SVD) and a new higher-order SVD (HOSVD) are
derived. Algorithms for computing new decompositions are provided. We also give
some numerical examples to illustrate our theoretical results.
