Optimization on Riemannian manifolds and applications
Description
Our work is to generalize Euclidean optimization algorithms to Riemannian manifolds. The applications are found in many areas, e.g., matrix completion problems, truss optimization, finite-element discretization of Cosserat rods, matrix mean computation, independent component analysis, image segmentation and recoginition, electrostatics and electronic structure calculation, finance and chemistry, multilinear algebra, low-rank learning, shape analysis and blind source separation.
People
Projects
- Broyden family optimization methods on Riemannian manifolds
- Trust Region with self-adjoint rank-one update on Riemannian manifolds
- Gradient sampling methods on Riemannian manifolds
- Soft dimension reduction for independent component analysis
- Synchronization of rotations via Riemannian optimizations
- Riemannian Quasi-Newton algorithms for computing reparameterization for elastic shape analysis
- Riemannian Quasi-Newton algorithms for computing elastic shape mean
- Elastic shape for facial variation and respirator fit
Publications
- Guifang Zhou, Wen Huang, Kyle A. Gallivan, Paul Van Dooren, Pierre-Antoine Absil. "Rank-Constrained Optimization: A Riemannian Manifold Approach", Accepted in European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2015).
- Wen Huang, Kyle A. Gallivan, Anuj Srivastava, Pierre-Antoine Absil. "Riemannian Optimization for Elastic Shape Analysis", Short version, The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014).
- Wen Huang, Pierre-Antoine Absil, Kyle A. Gallivan. "A Riemannian symmetric rank-one trust-region method", Mathematical Programming Series A and B, DOI:10.1007/s10107-014-0765-1.
Library