Rank One Completion for Higher Order Tensors
For researchers working on tensor completion, this provides a computationally efficient method for the rank-one case, though it is incremental relative to existing low-rank tensor completion approaches.
The paper introduces a recursive algorithm for rank one tensor completion that solves linear systems and computes singular vectors, achieving unique completion under noiseless conditions and robustness to small noise. Numerical experiments confirm efficiency and accuracy.
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This algorithm only requires solving linear systems and computing singular vectors. In the absence of noise, it produces a unique rank one completion under some assumptions. In the presence of noise, we show that the computed rank one tensor completion is close to the exact one when the noise is sufficiently small. Numerical experiments demonstrate the efficiency and accuracy of the proposed method.