Trace Ratio Optimization with an Application to Multi-view Learning
This work addresses a mathematical optimization problem with applications in multi-view learning, but it appears incremental as it builds on existing methods like Fisher linear discriminant analysis and canonical correlation analysis.
The paper tackles the trace ratio optimization problem on the Stiefel manifold, establishing theoretical conditions and proposing a convergent numerical method, with application to multi-view subspace learning showing efficiency and effectiveness on real-world datasets.
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.