Maximizing sum of coupled traces with applications

Li Wang, Lei Hong Zhang, Ren Cang Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper concerns maximizing the sum of coupled traces of quadratic and linear matrix forms. The coupling comes from requiring the matrix variables in the quadratic and linear matrix forms to be packed together to have orthonormal columns. At a maximum, the KKT condition becomes a nonlinear polar decomposition (NPD) of a matrix-valued function with dependency on the orthogonal polar factor. A self-consistent-field iteration, along with a locally optimal conjugate gradient (LOCG) acceleration, are proposed to compute the NPD. It is proved that both methods are convergent and it is demonstrated numerically that the LOCG acceleration is very effective. As applications, we demonstrate our methods on the MAXBET subproblem and the multi-view partially shared subspace learning (MvPS) subproblem, both of which sit at the computational kernels of two multi-view subspace learning models. In particular, we also demonstrate MvPS on several real world data sets.

Original languageEnglish
Pages (from-to)587-629
Number of pages43
JournalNumerische Mathematik
Volume152
Issue number3
DOIs
Publication statusPublished - Nov 2022
Externally publishedYes

Keywords

  • Coupled traces
  • Multi-view subspace learning
  • Nonlinear polar decomposition
  • NPD
  • SCF
  • Stiefel manifold

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