scholarly journals Low-rank tensor completion by Riemannian optimization

2013 ◽  
Vol 54 (2) ◽  
pp. 447-468 ◽  
Author(s):  
Daniel Kressner ◽  
Michael Steinlechner ◽  
Bart Vandereycken
Author(s):  
Tengfei Zhou ◽  
Hui Qian ◽  
Zebang Shen ◽  
Chao Zhang ◽  
Congfu Xu

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there is still room for improvement. To fill the gap, in this paper, a novel Riemannian model is proposed to tightly integrate the original model and the side information by overcoming their inconsistency. For this model, an efficient Riemannian conjugate gradient descent solver is devised based on a new metric that captures the curvature of the objective. Numerical experiments suggest that our method is more accurate than the state-of-the-art without compromising the efficiency.


Author(s):  
Tianheng Zhang ◽  
Jianli Zhao ◽  
Qiuxia Sun ◽  
Bin Zhang ◽  
Jianjian Chen ◽  
...  

2019 ◽  
Vol 73 ◽  
pp. 62-69 ◽  
Author(s):  
Wen-Hao Xu ◽  
Xi-Le Zhao ◽  
Teng-Yu Ji ◽  
Jia-Qing Miao ◽  
Tian-Hui Ma ◽  
...  

Author(s):  
Jize Xue ◽  
Yongqiang Zhao ◽  
Shaoguang Huang ◽  
Wenzhi Liao ◽  
Jonathan Cheung-Wai Chan ◽  
...  

2020 ◽  
Vol 31 (11) ◽  
pp. 4567-4581 ◽  
Author(s):  
Jize Xue ◽  
Yongqiang Zhao ◽  
Wenzhi Liao ◽  
Jonathan Cheung-Wai Chan ◽  
Seong G. Kong

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jinzhi Liao ◽  
Jiuyang Tang ◽  
Xiang Zhao ◽  
Haichuan Shang

POI recommendation finds significant importance in various real-life applications, especially when meeting with location-based services, e.g., check-ins social networks. In this paper, we propose to solve POI recommendation through a novel model of dynamic tensor, which is among the first triumphs of its kind. In order to carry out timely recommendation, we predict POI by utilizing a completion algorithm based on fast low-rank tensor. Particularly, the dynamic tensor structure is complemented by the fast low-rank tensor completion algorithm so as to achieve prediction with better performance, where the parameter optimization is achieved by a pigeon-inspired heuristic algorithm. In short, our POI recommendation via the dynamic tensor method can take advantage of the intrinsic characteristics of check-ins data due to the multimode features such as current categories, subsequent categories, and temporal information as well as seasons variations are all integrated into the model. Extensive experiment results not only validate the superiority of our proposed method but also imply the application prospect in large-scale and real-time POI recommendation environment.


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