Accelerating alternating least squares for tensor decomposition by pairwise perturbation

The alternating least squares (ALS) algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up quadratic optimization subproblems. We introduce a novel family of algorithms that uses perturbative corrections subproblems rather than recomputing contractions. This approximation accurate when factor matrices are changing little across iterations, which occurs ALS approaches convergence. provide theoretical analysis bound error. Our numerical experiments demonstrate proposed pairwise perturbation easy control converge minima as good ALS. experimental results show improvements 3.1 × with respect state-of-the-art various model problems real datasets.