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Generalized Higher-Order Orthogonal Iteration for Tensor Decomposition and Completion
Yuanyuan Liu · Fanhua Shang · Wei Fan · James Cheng · Hong Cheng

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None

Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for large-scale problems. To address this difficulty, we therefore propose an efficient and scalable core tensor Schatten 1-norm minimization method for simultaneous tensor decomposition and completion, with a much lower computational complexity. We first induce the equivalence relation of Schatten 1-norm of a low-rank tensor and its core tensor. Then the Schatten 1-norm of the core tensor is used to replace that of the whole tensor, which leads to a much smaller-scale matrix SNM problem. Finally, an efficient algorithm with a rank-increasing scheme is developed to solve the proposed problem with a convergence guarantee. Extensive experimental results show that our method is usually more accurate than the state-of-the-art methods, and is orders of magnitude faster.

Author Information

Yuanyuan Liu (The Chinese University of Hong Kong)
Fanhua Shang (The Chinese University of Hong Kong)
Wei Fan (Huawei Noah′s Ark Lab, Hong Kong)
James Cheng (The Chinese University of Hong Kong)
Hong Cheng (The Chinese University of Hong Kong)

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