Tensor and its tucker core: The invariance relationships

doi:10.1002/nla.2086

CORC > 上海财经大学 > 上海财经大学

	Tensor and its tucker core: The invariance relationships
	Jiang, Bo 1; Yang, Fan 2; Zhang, Shuzhong 3
刊名	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
	2017-05
卷号	24 期号:3
关键词	border rank CP decomposition tensor eigenvalues tensor Schatten quasi norm Tucker decomposition
ISSN号	1070-5325
DOI	10.1002/nla.2086
英文摘要	In one study, Hillar and Lim famously demonstrated that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are nondeterministic polynomial-time hard. Despite many recent advancements, the state-of-the-art methods for computing such tensor analogues still suffer severely from the curse of dimensionality. In this paper, we show that the Tucker core of a tensor, however, retains many properties of the original tensor, including the CANDECOMP/PARAFAC (CP) rank, the border rank, the tensor Schatten quasi norms, and the Z-eigenvalues. When the core tensor is smaller than the original tensor, this property leads to considerable computational advantages as confirmed by our numerical experiments. In our analysis, we in fact work with a generalized Tucker-like decomposition that can accommodate any full column-rank factor matrices.
WOS研究方向	Mathematics
语种	英语
出版者	WILEY
WOS记录号	WOS:000398683100007
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/996]
专题	上海财经大学
通讯作者	Jiang, Bo
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.Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA; 3.Univ Minnesota, Dept Ind & Syst Engn, Minneapolis, MN 55455 USA
推荐引用方式 GB/T 7714	Jiang, Bo,Yang, Fan,Zhang, Shuzhong. Tensor and its tucker core: The invariance relationships[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2017,24(3).
APA	Jiang, Bo,Yang, Fan,&Zhang, Shuzhong.(2017).Tensor and its tucker core: The invariance relationships.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,24(3).
MLA	Jiang, Bo,et al."Tensor and its tucker core: The invariance relationships".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 24.3(2017).