One-bit tensor completion via transformed tensor singular value decomposition

• Published in: Applied Mathematical Modelling 2021-07, Vol.95, p.760-782
• Main Authors: Hou, Jingyao, Zhang, Feng, Wang, Jianjun
• Format: Article
• Language: English
• Subjects: Algorithms; Errors; Linear invertible transforms; Linear transformations; Low-tubal-rank tensor; Lower bounds; Mathematical analysis; One-bit observations; Singular value decomposition; Tensor nuclear norm; Tensors; Upper bounds
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.02.032

•This work considers a tensor completion problem under the frame of tensor SVD, which is applied in many fields.•Our discussion is based on binary observations, which significantly differs from common researches.•A convex model with theoretical guarantees and an efficient algorithm are proposed.•Numerical experiments on real-world data show potential applications of our method. This paper considers the problem of low-tubal-rank tensor completion from incomplete one-bit observations. Our work is inspired by the recently proposed invertible linear transforms based tensor-tensor product and transformed tensor singular value decomposition (t-SVD). Under this framework, a tensor nuclear norm constrained maximum log-likelihood estimation model is proposed, which is convex and efficiently solved. The feasibility of the model is proved with an upper bound of the estimation error obtained. We also show a lower bound of the worst-case estimation error, which combing with the obtained upper bound demonstrates that the estimation error is nearly order-optimal. Furthermore, an algorithm based on the alternating direction multipliers method (ADMM) and non-monotone spectral projected-gradient (SPG) method is designed to solve the estimation model. Simulations are performed to show the effectiveness of the proposed method, and the applications to real-world data demonstrate the promising performance of the proposed method.