A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction

Xijun Ma, Chungen Shen, Li Wang, Lei Hong Zhang*, Ren Cang Li

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

As an extension of the traditional principal component analysis, the multi-view canonical correlation analysis (MCCA) aims at reducing m high dimensional random variables si∈ℝni(i=1,2,…,m) by proper projection matrices Xi∈ℝni×ℓ so that the m reduced ones yi=XiTsi∈ℝℓ have the “maximal correlation.” Various measures of the correlation for yi (i = 1,2,…,m) in MCCA have been proposed. One of the earliest criteria is the sum of all traces of pair-wise correlation matrices between yi and yj subject to the orthogonality constraints on Xi, i = 1,2,…,m. The resulting problem is to maximize a homogeneous quadratic function over the product of Stiefel manifolds and is referred to as the MAXBET problem. In this paper, the problem is first reformulated as a coupled nonlinear eigenvalue problem with eigenvector dependency (NEPv) and then solved by a novel self-consistent-field (SCF) iteration. Global and local convergences of the SCF iteration are studied and proven computational techniques in the standard eigenvalue problem are incorporated to yield more practical implementations. Besides the preliminary numerical evaluations on various types of synthetic problems, the efficiency of the SCF iteration is also demonstrated in an application to multi-view feature extraction for unsupervised learning.

Original languageEnglish
Article number13
Number of pages34
JournalAdvances in Computational Mathematics
Volume48
Issue number2
Early online date16 Mar 2022
DOIs
Publication statusPublished - Apr 2022

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • MAXBET
  • Multi-view canonical correlation analysis
  • Multi-view feature extraction
  • Nonlinear eigenvalue problem
  • Self-consistent-field iteration
  • Stiefel manifold

Cite this