A dual framework for low-rank tensor completion
This work addresses tensor completion for applications like data analysis, but it is incremental as it builds on existing latent trace norm methods.
The authors tackled the problem of low-rank tensor completion by proposing a variant of the latent trace norm to learn non-sparse combinations of tensors, developing a dual framework with a trust region algorithm that showed efficacy on real-world datasets.
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a variant of the latent trace norm that helps in learning a non-sparse combination of tensors. We develop a dual framework for solving the low-rank tensor completion problem. We first show a novel characterization of the dual solution space with an interesting factorization of the optimal solution. Overall, the optimal solution is shown to lie on a Cartesian product of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian optimization framework for proposing computationally efficient trust region algorithm. The experiments illustrate the efficacy of the proposed algorithm on several real-world datasets across applications.