Low-rank tensor completion based on non-convex logDet function and Tucker decomposition

秩(图论) 数学 张量(固有定义) 低秩近似 塔克分解 矩阵分解 计算机科学 矩阵范数 基质(化学分析)
作者
Chengfei Shi,Zhengdong Huang,Li Wan,Tifan Xiong
出处
期刊:Signal, Image and Video Processing [Springer Science+Business Media]
卷期号:15 (6): 1169-1177
标识
DOI:10.1007/s11760-020-01845-7
摘要

For the problem of low-rank tensor completion, rank estimation plays an extremely important role. And among some outstanding researches, nuclear norm is often used as a substitute of rank in the optimization due to its convex property. However, recent advances show that some non-convex functions could approximate the rank better, which can significantly improve the precision of the algorithm. While, the complexity of non-convex functions also leads to much higher computation cost, especially when the data are on a large scale. This paper proposes a mixture model for tensor completion by combining logDet function with Tucker decomposition, in which the logDet function is utilized as a much tighter rank approximation than the nuclear norm and the Tucker decomposition can significantly reduce the size of tensor that needs to be evaluated. In the implementation of the method, alternating direction method of multipliers is employed to obtain the optimal tensor completion. Several experiments are carried out to validate the effectiveness and efficiency of the method.
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