An extrapolation trust-region alternating least-squares algorithm for triple decomposition of third-order tensors

Triple decomposition, which is a novel decomposition for the third order tensors, decomposes a third order tensor into a product of three third order low rank tensors. Alternating least-squares (ALS) is one of the most commonly used algorithms for tensor decomposition. In this paper, we combined the trust region method with the ALS algorithm to establish an extrapolation trust-region alternating least-squares algorithm for triple decomposition (TD-ETRALS). Different from the fixed regularization parameters in the modified alternating least-squares method (EMALS), TD-ETRALS adjusts the trust-region parameters in each iteration to achieve the preset accuracy of triple decomposition faster and more accurately. Theoretically, we prove that the sequence generated by TD-ETRALS converges to a critical point. Numerical experiments show that TD-ETRALS preforms better than EMALS in triple decomposition for the tensors generated by a uniform distribution in the relatively narrow interval and the tensors with Gaussian noise. In the example of image processing, TD-ETRALS also shows some advantages in low rank decomposition.