Tensor maximal correlation problems



This paper studies the tensor maximal correlation problem, which aims at optimizing correlations between sets of variables in many statistical applications. We reformulate the problem as an equivalent polynomial optimization problem, by adding the first order optimality condition to the constraints, then construct a hierarchy of semidefinite relaxations for solving it. The global maximizers of the problem can be detected by solving a finite number of such semidefinite relaxations. Numerical experiments show the efficiency of the proposed method.


Tensor maximal correlation problems Polynomial optimization Lasserre relaxation Semidefinite program 

Mathematics Subject Classification

62H20 65K05 90C22 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  3. 3.School of Mathematical Sciences, and MOE-LSCShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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