Tensor maximal correlation problems

Anwa Zhou (), Xin Zhao (), Jinyan Fan () and Yanqin Bai ()
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Anwa Zhou: Shanghai University
Xin Zhao: Shanghai Jiao Tong University
Jinyan Fan: Shanghai Jiao Tong University
Yanqin Bai: Shanghai University

Journal of Global Optimization, 2018, vol. 70, issue 4, No 7, 843-858

Abstract: Abstract 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.

Keywords: Tensor maximal correlation problems; Polynomial optimization; Lasserre relaxation; Semidefinite program; 62H20; 65K05; 90C22 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-017-0592-z

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