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| The regularization method could deal with the swamp effect of alternating least squares (ALS) algorithms for tensor decomposition. The regularization term is a norm of the difference between the solution and the current iterate. In this paper, we show that the norm could be weakened to a seminorm so the selection of the regularization term could be more flexible. To overcome the swamp effect and avoid the drawback that the Hessian of the subproblem may get close to singular in the iterative procedure, we propose a seminorm regularized ALS algorithm for solving the canonical tensor decomposition. %In computation, the seminorm regularization term is added conveniently by replacing the Hessian %by its modified eigenvalue decomposition or the modified Cholesky factorization. Moreover, in new algorithm, we introduce a novel extrapolation in the update of each mode factor which makes an immediate impression on the update of subsequent ones. Under some mild assumptions, the global convergence of new algorithm with a seminorm regularization and the novel extrapolation is established. Numerical experiments on synthetic and real-world problems show that the new method is efficient and promising. |
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| Keywords: Alternating least squares, CANDECOMP, PARAFAC, regularization method, tensor decomposition. |
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