Rank Minimization on Tensor Ring: A New Paradigm in Scalable Tensor Decomposition and Completion
This addresses scalability issues in tensor completion for applications like data analysis, though it is incremental as it builds on existing tensor ring methods.
The paper tackles the high computational cost and sensitivity in low-rank tensor completion by proposing a new model based on tensor ring decomposition with convex surrogates, resulting in high performance and efficiency as shown in experiments on synthetic and real-world data.
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high sensitivity of model complexity. In this paper, taking advantages of high compressibility of the recently proposed tensor ring (TR) decomposition, we propose a new model for tensor completion problem. This is achieved through introducing convex surrogates of tensor low-rank assumption on latent tensor ring factors, which makes it possible for the Schatten norm regularization based models to be solved at much smaller scale. We propose two algorithms which apply different structured Schatten norms on tensor ring factors respectively. By the alternating direction method of multipliers (ADMM) scheme, the tensor ring factors and the predicted tensor can be optimized simultaneously. The experiments on synthetic data and real-world data show the high performance and efficiency of the proposed approach.