Krylov-Levenberg-Marquardt Algorithm for Structured Tucker Tensor Decompositions

Structured Tucker tensor decomposition models complete or incomplete multiway data sets (tensors), where the core tensor and the factor matrices can obey different constraints. The model includes block-term decomposition or canonical polyadic decomposition as special cases. We propose a very flexible optimization method for the structured Tucker decomposition problem, based on the second-order Levenberg-Marquardt optimization, using an approximation of the Hessian matrix by the Krylov subspace method. An algorithm with limited sensitivity of the decomposition is included. The proposed algorithm is shown to perform well in comparison to existing tensor decomposition methods.

Automated summary

The structured Tucker tensor decomposition model can handle multiway data sets with different constraints. A flexible optimization method based on the second-order Levenberg-Marquardt optimization is proposed for this model, demonstrating good performance compared to existing tensor decomposition methods.