NDLI: Accelerated singular value thresholding for matrix completion

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Accelerated singular value thresholding for matrix completion

Content Provider	ACM Digital Library
Author	Hu, Yao Liu, Jun He, Xiaofei Zhang, Debing Ye, Jieping
Abstract	Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real world applications, such as recommender system and image in-painting. These problems can be formulated as a general matrix completion problem. The Singular Value Thresholding (SVT) algorithm is a simple and efficient first-order matrix completion method to recover the missing values when the original data matrix is of low rank. SVT has been applied successfully in many applications. However, SVT is computationally expensive when the size of the data matrix is large, which significantly limits its applicability. In this paper, we propose an Accelerated Singular Value Thresholding (ASVT) algorithm which improves the convergence rate from O(1/N) for SVT to $O(1/N^{2}),$ where N is the number of iterations during optimization. Specifically, the dual problem of the nuclear norm minimization problem is derived and an adaptive line search scheme is introduced to solve this dual problem. Consequently, the optimal solution of the primary problem can be readily obtained from that of the dual problem. We have conducted a series of experiments on a synthetic dataset, a distance matrix dataset and a large movie rating dataset. The experimental results have demonstrated the efficiency and effectiveness of the proposed algorithm.
Starting Page	298
Ending Page	306
Page Count	9
File Format	PDF MP4
ISBN	9781450314626
DOI	10.1145/2339530.2339581
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-08-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Singular value thresholding Nesterov's method Adaptive line search scheme Matrix completion
Content Type	Audio Text
Resource Type	Article

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