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.
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Anwa Zhou was partially supported by the NSFC Grant 11701356, the National Postdoctoral Program for Innovative Talents Grant BX201600097 and Project Funded by China Postdoctoral Science Foundation Grant 2016M601562. Jinyan Fan was partially supported by the NSFC Grant 11571234. Yanqin Bai was partially supported by the NSFC Grant 11771275.
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Zhou, A., Zhao, X., Fan, J. et al. Tensor maximal correlation problems. J Glob Optim 70, 843–858 (2018). https://doi.org/10.1007/s10898-017-0592-z
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DOI: https://doi.org/10.1007/s10898-017-0592-z