A dual framework for low-rank tensor completion
M. Nimishakavi, P. Jawanpuria, and B. Mishra
We propose a novel formulation of the low-rank tensor completion problem that is based on the duality theory and a particular choice of low-rank regularizer. This low-rank regularizer along with the dual perspective provides a simple characterization of the solution to the tensor completion problem. Motivated by large-scale setting, we next derive a rank-constrained reformulation of the proposed optimization problem, which is shown to lie on the Riemannian spectrahedron manifold. We exploit the versatile Riemannian optimization framework to develop computationally efficient conjugate gradient and trust-region algorithms. The experiments confirm the benefits of our choice of regularization and the proposed algorithms outperform state-of-the-art algorithms on several real-world data sets in different applications.
- Status: Technical report, 2017. A shorter version got accepted to the NIPS workshop on Synergies in Geometric Data Analysis, 2017.
- Paper: [arXiv:1712.01193].
- Matlab code: dual_tensor_completion_18Feb2018.zip
- 18 Feb 2018: added the codes for the primal fixed-rank latent tensor norm formulation.
- 04 December 2017: code is online.