Weighted Krylov-Levenberg-Marquardt Method for Canonical Polyadic Tensor Decomposition

Weighted canonical polyadic (CP) tensor decomposition appears in a wide range of applications. A typical situation where the weighted decomposition is needed is when some tensor elements are unknown, and the task is to fill in the missing elements under the assumption that the tensor admits a low-rank model. The traditional methods for large-scale decomposition tasks are based on alternating least-squares methods or gradient methods. Second-order methods might have significantly better convergence, but so far they were used only on small tensors. The proposed Krylov-Levenberg-Marquardt method enables to do second-order-based iterations even in large-scale decomposition problems, with or without weights. We show in simulations that the proposed technique can outperform existing state-of-the-art algorithms in some scenarios.