Trace ratio optimization with an application to multi-view learning

• 成果类型: Article
• 署名作者: Wang, Li; Zhang, Lei-Hong; Li, Ren-Cang
• 署名单位: University of Texas System; University of Texas Arlington; University of Texas System; University of Texas Arlington; Soochow University - China; Hong Kong Baptist University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01900-w
• 发表日期: 2023
• 页码: 97-131
• 关键词: perturbation bounds; procrustes; CONVERGENCE; algorithms; rotation; unitary

摘要

A trace ratio optimization problem over the Stiefel manifold is investigated from the perspectives of both theory and numerical computations. Necessary conditions in the form of nonlinear eigenvalue problem with eigenvector dependency (NEPv) are established and a numerical method based on the self-consistent field (SCF) iteration with a postprocessing step is designed to solve the NEPv and the method is proved to be always convergent. As an application to multi-view subspace learning, a new framework and its instantiated concrete models are proposed and demonstrated on real world data sets. Numerical results show that the efficiency of the proposed numerical methods and effectiveness of the new orthogonal multi-view subspace learning models.