  In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined
canonical polyadic decomposition (CPD), are easily to implement and can be
extended to higher order CPD. Unfortunately, the algorithms become
computationally demanding, and they are often not applicable to higher order
and relatively large scale tensors. In this paper, by exploiting the uniqueness
of CPD and the relation of a tensor in Kruskal form and its unfolded tensor, we
propose a fast approach to deal with this problem. Instead of directly
factorizing the high order data tensor, the method decomposes an unfolded
tensor with lower order, e.g., order-3 tensor. On basis of the order-3
estimated tensor, a structured Kruskal tensor of the same dimension as the data
tensor is then generated, and decomposed to find the final solution using fast
algorithms for the structured CPD. In addition, strategies to unfold tensors
are suggested and practically verified in the paper.
