  In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some
difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when
the loading components are highly collinear in several or all modes, or when
CPD does not have an optimal solution. In such the cases, norms of some rank-1
terms become significantly large and cancel each other. This makes algorithms
getting stuck in local minima while running a huge number of iterations does
not improve the decomposition. In this paper, we propose an error preservation
correction method to deal with such problem. Our aim is to seek a new tensor
whose norms of rank-1 tensor components are minimised in an optimization
problem, while it preserves the approximation error. An alternating correction
algorithm and an all-atone algorithm have been developed for the problem. In
addition, we propose a novel CPD with a bound constraint on a norm of the
rank-one tensors. The method can be useful for decomposing tensors that cannot
be analyzed by traditional algorithms, such as tensors corresponding to the
matrix multiplication.
