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	A new retraction for accelerating the Riemannian three-factor low-rank matrix completion algorithm
	Li, Zhizhong ; Zhao, Deli ; Lin, Zhouchen ; Chang, Edward Y.
	2015
英文摘要	The Riemannian three-factor matrix completion (R3MC) algorithm is one of the state-of-the-art geometric optimization methods for the low-rank matrix completion problem. It is a nonlinear conjugate-gradient method optimizing on a quotient Riemannian manifold. In the line search step, R3MC approximates the minimum point on the searching curve by minimizing on the line tangent to the curve. However, finding the exact minimum point by iteration is too expensive. We address this issue by proposing a new retraction with a minimizing property. This special property provides the exact minimization for the line search by establishing correspondences between points on the searching curve and points on the tangent line. Accelerated R3MC, which is R3MC equipped with this new retraction, outperforms the original algorithm and other geometric algorithms for matrix completion in our empirical study. ? 2015 IEEE.; EI; 4530-4538; 07-12-June-2015
语种	英语
出处	EI
出版者	IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2015
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/436561]
专题	数学科学学院 信息科学技术学院
推荐引用方式 GB/T 7714	Li, Zhizhong,Zhao, Deli,Lin, Zhouchen,et al. A new retraction for accelerating the Riemannian three-factor low-rank matrix completion algorithm. 2015-01-01.

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