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• W2404467465 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 SIAM International Conference on Data Mining (SDM)Factor Matrix Trace Norm Minimization for Low-Rank Tensor CompletionYuanyuan Liu, Fanhua Shang, Hong Cheng, James Cheng, and Hanghang TongYuanyuan LiuDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Computer Science Department, City College, The City University of New York.Search for more papers by this author, Fanhua ShangDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Computer Science Department, City College, The City University of New York.Search for more papers by this author, Hong ChengDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Computer Science Department, City College, The City University of New York.Search for more papers by this author, James ChengDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Computer Science Department, City College, The City University of New York.Search for more papers by this author, and Hanghang TongDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongDepartment of Computer Science and Engineering, The Chinese University of Hong Kong.Computer Science Department, City College, The City University of New York.Search for more papers by this authorpp.866 - 874Chapter DOI:https://doi.org/10.1137/1.9781611973440.99PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Most existing low-n-rank minimization algorithms for tensor completion suffer from high computational cost due to involving multiple singular value decompositions (SVDs) at each iteration. To address this issue, we propose a novel factor matrix trace norm minimization method for tensor completion problems. Based on the CANDECOMP/PARAFAC (CP) decomposition, we first formulate a factor matrix rank minimization model by deducing the relation between the rank of each factor matrix and the mode-n rank of a tensor. Then, we introduce a tractable relaxation of our rank function, which leads to a convex combination problem of much smaller scale matrix nuclear norm minimization. Finally, we develop an efficient alternating direction method of multipliers (ADMM) scheme to solve the proposed problem. Experimental results on both synthetic and real-world data validate the effectiveness of our approach. Moreover, our method is significantly faster than the state-of-the-art approaches and scales well to handle large datasets. Previous chapter Next chapter RelatedDetails Published:2014eISBN:978-1-61197-344-0 https://doi.org/10.1137/1.9781611973440Book Series Name:ProceedingsBook Code:PRDT14Book Pages:1-1086" @default.
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• W2404467465 title "Factor Matrix Trace Norm Minimization for Low-Rank Tensor Completion" @default.
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