Tensor principal component analysis via convex optimization

doi:10.1007/s10107-014-0774-0

CORC > 上海财经大学 > 上海财经大学

	Tensor principal component analysis via convex optimization
	Jiang, Bo 1; Ma, Shiqian 2; Zhang, Shuzhong 3
刊名	MATHEMATICAL PROGRAMMING
	2015-05
卷号	150 期号:2 页码:423-457
关键词	Tensor Principal component analysis Low rank Nuclear norm Semidefinite programming relaxation
ISSN号	0025-5610
DOI	10.1007/s10107-014-0774-0
英文摘要	This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case where the tensor in question is super-symmetric with an even degree. In that case, the tensor can be embedded into a symmetric matrix. We prove that if the tensor is rank-one, then the embedded matrix must be rank-one too, and vice versa. The tensor PCA problem can thus be solved by means of matrix optimization under a rank-one constraint, for which we propose two solution methods: (1) imposing a nuclear norm penalty in the objective to enforce a low-rank solution; (2) relaxing the rank-one constraint by semidefinite programming. Interestingly, our experiments show that both methods can yield a rank-one solution for almost all the randomly generated instances, in which case solving the original tensor PCA problem to optimality. To further cope with the size of the resulting convex optimization models, we propose to use the alternating direction method of multipliers, which reduces significantly the computational efforts. Various extensions of the model are considered as well.
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000351522700008
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/1554]
专题	上海财经大学
通讯作者	Ma, Shiqian
作者单位	1.Shanghai Univ Finance & Econ, Sch Informat Management & Engn, Res Ctr Management Sci & Data Analyt, Shanghai 200433, Peoples R China; 2.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China; 3.Univ Minnesota, Dept Ind & Syst Engn, Minneapolis, MN 55455 USA
推荐引用方式 GB/T 7714	Jiang, Bo,Ma, Shiqian,Zhang, Shuzhong. Tensor principal component analysis via convex optimization[J]. MATHEMATICAL PROGRAMMING,2015,150(2):423-457.
APA	Jiang, Bo,Ma, Shiqian,&Zhang, Shuzhong.(2015).Tensor principal component analysis via convex optimization.MATHEMATICAL PROGRAMMING,150(2),423-457.
MLA	Jiang, Bo,et al."Tensor principal component analysis via convex optimization".MATHEMATICAL PROGRAMMING 150.2(2015):423-457.