On the Nuclear Norm and the Singular Value Decomposition of Tensors

被引：0
|
作者：
Harm Derksen
机构：
[1] University of Michigan,Department of Mathematics
来源：
Foundations of Computational Mathematics | 2016年 / 16卷
关键词：
Tensor decomposition; Nuclear norm; Singular value decomposition; PARAFAC; CANDECOMP; 15A69; 15A18;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Finding the rank of a tensor is a problem that has many applications. Unfortunately, it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of the rank of a tensor. We determine the nuclear norm of various tensors of interest. Along the way, we also do a systematic study various measures of orthogonality in tensor product spaces and we give a new generalization of the singular value decomposition to higher-order tensors.
引用
收藏
页码：779 / 811
页数：32
相关论文
共 50 条
  • [21] SINGULAR VALUE SCREENING RULES FOR THE NUCLEAR NORM REGULARIZED MULTIVARIATE LINEAR REGRESSION
    Shang, Pan
    Kong, Lingchen
    PACIFIC JOURNAL OF OPTIMIZATION, 2021, 17 (01): : 1 - 22
  • [22] L1-NORM HIGHER-ORDER SINGULAR-VALUE DECOMPOSITION
    Markopoulos, Panos P.
    Chachlakis, Dimitris G.
    Prater-Bennette, Ashley
    2018 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2018), 2018, : 1353 - 1357
  • [23] Singular value inclusion sets for rectangular tensors
    Zhao, Jianxing
    Li, Chaoqian
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (07): : 1333 - 1350
  • [24] Generalized Singular Value Decompositions for Tensors and Their Applications
    He, Zhuo-Heng
    Ng, Michael K.
    Zeng, Chao
    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2021, 14 (03): : 692 - 713
  • [25] Singular value inclusion sets of rectangular tensors
    Yao, Hongmei
    Zhang, Can
    Liu, Lei
    Zhou, Jiang
    Bu, Changjiang
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 576 : 181 - 199
  • [26] Z-singular value and Z-singular value inclusion sets for tensors
    Yun Miao
    Chaoqian Li
    Yimin Wei
    Japan Journal of Industrial and Applied Mathematics, 2019, 36 : 1055 - 1087
  • [27] Convex Recovery of Tensors Using Nuclear Norm Penalization
    Chretien, Stephane
    Wei, Tianwen
    LATENT VARIABLE ANALYSIS AND SIGNAL SEPARATION, LVA/ICA 2015, 2015, 9237 : 360 - 367
  • [28] Singular value decomposition and similarity renormalization group evolution of nuclear interactions
    Zhu, B.
    Wirth, R.
    Hergert, H.
    PHYSICAL REVIEW C, 2021, 104 (04)
  • [29] Z-singular value and Z-singular value inclusion sets for tensors
    Miao, Yun
    Li, Chaoqian
    Wei, Yimin
    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2019, 36 (03) : 1055 - 1087
  • [30] Object Recognition with the Higher-Order Singular Value Decomposition of the Multi-dimensional Prototype Tensors
    Cyganek, Boguslaw
    MODERN TRENDS AND TECHNIQUES IN COMPUTER SCIENCE (CSOC 2014), 2014, 285 : 395 - 405
12345