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M-estimation in Low-rank Matrix Factorization: a General Framework

Tu, Wei, Liu, Peng, Zhao, Jingyu, Liu, Yi, Kong, Linglong, Li, Guodong, Jiang, Bei, Tian, Guangjian, Yao, Hengshuai (2020) M-estimation in Low-rank Matrix Factorization: a General Framework. In: Proceedings: 2019 IEEE International Conference on Data Mining. 2019 IEEE International Conference on Data Mining. . pp. 568-577. IEEE ISBN 978-1-72814-603-4. (doi:10.1109/ICDM.2019.00067)

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http://dx.doi.org/10.1109/ICDM.2019.00067

Abstract

Many 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.

Item Type: Conference or workshop item (Proceeding)
DOI/Identification number: 10.1109/ICDM.2019.00067
Uncontrolled keywords: matrix recovery, M-estimation, matrix factorisation, robustness, statistical foundation
Subjects: T Technology > TK Electrical engineering. Electronics. Nuclear engineering
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Peng Liu
Date Deposited: 09 Aug 2019 10:55 UTC
Last Modified: 11 Feb 2020 11:05 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/75738 (The current URI for this page, for reference purposes)
Liu, Peng: https://orcid.org/0000-0002-0492-0029
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