On the Convergence of Alternating Least Squares Optimisation in Tensor Format Representations
Provides a theoretical convergence analysis for a widely used tensor approximation method, benefiting researchers in high-dimensional numerical computation.
The paper analyzes the convergence of the alternating least squares algorithm for arbitrary tensor format representations, leveraging multilinearity to establish theoretical guarantees. No concrete numerical results are provided.
The approximation of tensors is important for the efficient numerical treatment of high dimensional problems, but it remains an extremely challenging task. One of the most popular approach to tensor approximation is the alternating least squares method. In our study, the convergence of the alternating least squares algorithm is considered. The analysis is done for arbitrary tensor format representations and based on the multiliearity of the tensor format. In tensor format representation techniques, tensors are approximated by multilinear combinations of objects lower dimensionality. The resulting reduction of dimensionality not only reduces the amount of required storage but also the computational effort.