Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data

被引:28
作者
Tan, Huachun [1 ]
Feng, Jianshuai [1 ]
Chen, Zhengdong [2 ]
Yang, Fan [3 ]
Wang, Wuhong [1 ]
机构
[1] Beijing Inst Technol, Dept Transportat Engn, Beijing 100081, Peoples R China
[2] Elect Engn Inst Hefei, Hefei 230037, Anhui, Peoples R China
[3] Univ Wisconsin, Dept Civil & Environm Engn, Madison, WI 53705 USA
基金
北京市自然科学基金; 中国国家自然科学基金;
关键词
TOOLBOX;
D O I
10.1155/2014/157597
中图分类号
O414.1 [热力学];
学科分类号
摘要
The problem of missing data in multiway arrays (i.e., tensors) is common in many fields such as bibliographic data analysis, image processing, and computer vision. We consider the problems of approximating a tensor by another tensor with low multilinear rank in the presence of missing data and possibly reconstructing it (i.e., tensor completion). In this paper, we propose a weighted Tucker model which models only the known elements for capturing the latent structure of the data and reconstructing the missing elements. To treat the nonuniqueness of the proposed weighted Tucker model, a novel gradient descent algorithm based on a Grassmann manifold, which is termed Tucker weighted optimization (Tucker-Wopt), is proposed for guaranteeing the global convergence to a local minimum of the problem. Based on extensive experiments, Tucker-Wopt is shown to successfully reconstruct tensors with noise and up to 95% missing data. Furthermore, the experiments on traffic flow volume data demonstrate the usefulness of our algorithm on real-world application.
引用
收藏
页数:12
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