An augmented Lagrangian algorithm for decomposition of symmetric tensors of order-4

Decomposition of symmetric tensors has found numerous applications in blind sources separation, blind identification, clustering, and analysis of social interactions. In this paper, we consider fourth order symmetric tensors, and its symmetric tensor decomposition. By imposing unit-length constraints on components, we resort the optimisation problem to the constrained eigenvalue decomposition in which eigenvectors are represented in form of rank-1 matrices. To this end, we develop an augmented Lagrangian algorithm with simple update rules. The proposed algorithm has been compared with the Trust-Region solver over manifold, and achieved higher success rates. The algorithm is also validated for blind identification, and achieves more stable results than the ALSCAF algorithm.