  In this paper, we define a semi-tensor product for third-order tensors. Based
on this definition, we present a new type of tensor decomposition strategy and
give the specific algorithm. This decomposition strategy actually generalizes
the tensor SVD based on semi-tensor product. Due to the characteristic of
semi-tensor product for compressing the data scale, we can therefore achieve
data compression in this way. Numerical comparisons are given to show the
advantages of this decomposition.
