QQ客服 官方微博 反馈留言

	Pushing the limits of affine rank minimization by adapting probabilistic PCA
	Xin, Bo ; Wipf, David
	2015
英文摘要	Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical conditions elucidate when this replacement is likely to be successful, they are highly restrictive and convex algorithms fail when the ambient rank is too high or when the constraint set is poorly structured. Non-convex alternatives fare somewhat better when carefully tuned; however, convergence to locally optimal solutions remains a continuing source of failure. Against this backdrop we derive a deceptively simple and parameter-free probabilistic PCA-like algorithm that is capable, over a wide battery of empirical tests, of successful recovery even at the theoretical limit where the number of measurements equals the degrees of freedom in the unknown low-rank matrix. Somewhat surprisingly, this is possible even when the affine constraint set is highly ill-conditioned. While proving general recovery guarantees remains evasive for non-convex algorithms, Bayesian-inspired or otherwise, we nonetheless show conditions whereby the underlying cost function has a unique stationary point located at the global optimum; no existing cost function we are aware of satisfies this property. The algorithm has also been successfully deployed on a computer vision application involving image rectification and a standard collaborative filtering benchmark.; EI; 419-427; 1
语种	英语
出处	32nd International Conference on Machine Learning, ICML 2015
内容类型	其他
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/436992]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Xin, Bo,Wipf, David. Pushing the limits of affine rank minimization by adapting probabilistic PCA. 2015-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。