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Conference Paper: M-estimation in Low-Rank Matrix Factorization: A General Framework

TitleM-estimation in Low-Rank Matrix Factorization: A General Framework
Authors
Keywordsmatrix recovery
M-estimation
matrix factorization
robustness
statistical foundation
Issue Date2019
PublisherIEEE, Computer Society. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000179
Citation
2019 IEEE International Conference on Data Mining (ICDM), Beijing, China, 8-11 November 2019, p. 568-577 How to Cite?
AbstractMany problems in science and engineering can be reduced to the recovery of an unknown large matrix from a small number of random linear measurements. Matrix factorization arguably is the most popular approach for low-rank matrix recovery. Many methods have been proposed using different loss functions, for example the most widely used L 2 loss, more robust choices such as L 1 and Huber loss, quantile and expectile loss for skewed data. All of them can be unified into the framework of M-estimation. In this paper, we present a general framework of low-rank matrix factorization based on M-estimation in statistics. The framework mainly involves two steps: firstly we apply Nesterov's smoothing technique to obtain an optimal smooth approximation for non-smooth loss function, such as L 1 and quantile loss; secondly we exploit an alternative updating scheme along with Nesterov's momentum method at each step to minimize the smoothed loss function. Strong theoretical convergence guarantee has been developed for the general framework, and extensive numerical experiments have been conducted to illustrate the performance of proposed algorithm.
Persistent Identifierhttp://hdl.handle.net/10722/286648
ISBN

 

DC FieldValueLanguage
dc.contributor.authorTu, W-
dc.contributor.authorLiu, P-
dc.contributor.authorZhao, J-
dc.contributor.authorLiu, Y-
dc.contributor.authorKong, L-
dc.contributor.authorLi, G-
dc.contributor.authorJiang, B-
dc.contributor.authorTian, G-
dc.contributor.authorYao, H-
dc.date.accessioned2020-09-04T13:28:32Z-
dc.date.available2020-09-04T13:28:32Z-
dc.date.issued2019-
dc.identifier.citation2019 IEEE International Conference on Data Mining (ICDM), Beijing, China, 8-11 November 2019, p. 568-577-
dc.identifier.isbn1550-4786-
dc.identifier.urihttp://hdl.handle.net/10722/286648-
dc.description.abstractMany problems in science and engineering can be reduced to the recovery of an unknown large matrix from a small number of random linear measurements. Matrix factorization arguably is the most popular approach for low-rank matrix recovery. Many methods have been proposed using different loss functions, for example the most widely used L 2 loss, more robust choices such as L 1 and Huber loss, quantile and expectile loss for skewed data. All of them can be unified into the framework of M-estimation. In this paper, we present a general framework of low-rank matrix factorization based on M-estimation in statistics. The framework mainly involves two steps: firstly we apply Nesterov's smoothing technique to obtain an optimal smooth approximation for non-smooth loss function, such as L 1 and quantile loss; secondly we exploit an alternative updating scheme along with Nesterov's momentum method at each step to minimize the smoothed loss function. Strong theoretical convergence guarantee has been developed for the general framework, and extensive numerical experiments have been conducted to illustrate the performance of proposed algorithm.-
dc.languageeng-
dc.publisherIEEE, Computer Society. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000179-
dc.relation.ispartofIEEE International Conference on Data Mining Proceedings-
dc.rightsIEEE International Conference on Data Mining Proceedings. Copyright © IEEE, Computer Society.-
dc.rights©2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.-
dc.subjectmatrix recovery-
dc.subjectM-estimation-
dc.subjectmatrix factorization-
dc.subjectrobustness-
dc.subjectstatistical foundation-
dc.titleM-estimation in Low-Rank Matrix Factorization: A General Framework-
dc.typeConference_Paper-
dc.identifier.emailLi, G: gdli@hku.hk-
dc.identifier.authorityLi, G=rp00738-
dc.identifier.doi10.1109/ICDM.2019.00067-
dc.identifier.scopuseid_2-s2.0-85078874206-
dc.identifier.hkuros313959-
dc.identifier.spage568-
dc.identifier.epage577-
dc.publisher.placeUnited States-

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