Trace Ratio Optimization with an Application to Multi-view Learning

2021/01/12 by Li Wang, Wang, Li, Lei‐Hong Zhang +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Machine Learning (cs.LG) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2101.04292

openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A trace ratio optimization problem over the Stiefel manifold is investigated from the perspectives of both theory and numerical computations. At least three special cases of the problem have arisen from Fisher linear discriminant analysis, canonical correlation analysis, and unbalanced Procrustes problem, respectively. Necessary conditions in the form of nonlinear eigenvalue problem with eigenvector dependency are established and a numerical method based on the self-consistent field (SCF) iteration is designed and 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 multi-view subspace learning models.

Citations

• A Self-consistent-field Iteration for Orthogonal Canonical Correlation Analysis

Related

• A Theory of the NEPv Approach for Optimization On the Stiefel Manifold
• A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold
• Sequential subspace methods on Stiefel manifold optimization
• Orthogonal Trace-Sum Maximization: Applications, Local Algorithms, and Global Optimality
• Nonlinear Eigen-approach ADMM for Sparse Optimization on Stiefel Manifold