A dual framework for low-rank tensor completion

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.Comment: Aceepted to appear in Advances of Nueral Information Processing Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on Synergies in Geometric Data Analysis 201

Inductive Framework for Multi-Aspect Streaming Tensor Completion with Side Information

Low rank tensor completion is a well studied problem and has applications in various fields. However, in many real world applications the data is dynamic, i.e., new data arrives at different time intervals. As a result, the tensors used to represent the data grow in size. Besides the tensors, in many real world scenarios, side information is also available in the form of matrices which also grow in size with time. The problem of predicting missing values in the dynamically growing tensor is called dynamic tensor completion. Most of the previous work in dynamic tensor completion make an assumption that the tensor grows only in one mode. To the best of our Knowledge, there is no previous work which incorporates side information with dynamic tensor completion. We bridge this gap in this paper by proposing a dynamic tensor completion framework called Side Information infused Incremental Tensor Analysis (SIITA), which incorporates side information and works for general incremental tensors. We also show how non-negative constraints can be incorporated with SIITA, which is essential for mining interpretable latent clusters. We carry out extensive experiments on multiple real world datasets to demonstrate the effectiveness of SIITA in various different settings