A further improvement of a fast damped Gauss-Newton algorithm for candecomp-parafac tensor decomposition

In this paper, a novel implementation of the damped Gauss-Newton algorithm (also known as Levenberg-Marquart) for the CANDECOMP-PARAFAC (CP) tensor decomposition is proposed. The method is based on a fast inversion of the approximate Hessian for the problem. It is shown that the inversion can be computed on O(NR⁶) operations, where N and R is the tensor order and rank, respectively. It is less than in the best existing state-of-the art algorithm with O(N³R⁶) operations. The damped Gauss-Newton algorithm is suitable namely for difficult scenarios, where nearly-colinear factors appear in several modes simultaneously. Performance of the method is shown on decomposition of large tensors (100 × 100 × 100 and 100 × 100 × 100 × 100) of rank 5 to 90.