On Approximation Algorithm for Orthogonal Low-Rank Tensor Approximation

This work studies solution methods for approximating a given tensor by sum of R rank-1 tensors with one or more the latent factors being orthonormal. Such problem arises from applications such as image processing, joint singular value decomposition, and independent component analysis. Most existing algorithms are iterative type, while approximation type limited. By exploring multilinearity orthogonality problem, we introduce an algorithm in this work. Depending on computation several key subproblems, proposed can be either deterministic randomized. The lower bound is established, both expected senses. ratio depends size tensor, number terms, data. When reduced to case, coincides those literature. Moreover, presented results fill gap left Yang (SIAM J Matrix Anal Appl 41:1797–1825, 2020), where that was established when there only orthonormal factor. Numerical show usefulness algorithm.