HYBRID ALTERNATING EXTRA-GRADIENT AND NEWTON'S METHOD FOR TENSOR DECOMPOSITION

This paper considers modified versions of the alternating least-squares (ALS) and the regularized alternating least-squares (RALS) algorithms for tensor decomposition. We propose two hybrid alternating methods by combining the extra-gradient method with Newton's method, where at eacah subproblem, the correction step of the extra-gradient is replaced by a Newton step. Theoretically, the step-size of the correction step can be possibly chosen in a wide range. Under certain assumptions, we analyze the global convergence of our algorithm. Preliminary numerical experiments show the effectiveness of the proposed methods, compared to the standard ALS and RALS algorithms.

Automated summary

This paper examines modified versions of ALS and RALS algorithms for tensor decomposition. Two hybrid alternating methods, which combine the extra-gradient method with Newton's method, are proposed. The global convergence of the algorithm is analyzed under certain assumptions, and preliminary numerical experiments demonstrate the effectiveness of the proposed methods compared to standard ALS and RALS algorithms.