| Paper ID | SPTM-21.6 |
| Paper Title |
A GLOBAL CAYLEY PARAMETRIZATION OF STIEFEL MANIFOLD\\FOR DIRECT UTILIZATION OF OPTIMIZATION MECHANISMS OVER VECTOR SPACES |
| Authors |
Keita Kume, Isao Yamada, Tokyo Institute of Technology, Japan |
| Session | SPTM-21: Optimization Methods for Signal Processing |
| Location | Gather.Town |
| Session Time: | Friday, 11 June, 13:00 - 13:45 |
| Presentation Time: | Friday, 11 June, 13:00 - 13:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [OPT] Optimization Methods for Signal Processing |
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| Virtual Presentation |
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| Abstract |
Optimization problem with orthogonality constraints, whose feasible region is called the Stiefel manifold, has rich applications in data sciences. The severe non-linearity of the Stiefel manifold has hindered the utilization of optimization mechanisms developed specially over a vector space for the problem. In this paper, we present a global parametrization of the Stiefel manifold entirely by a single fixed vector space with the Cayley transform, say Global Cayley Parametrization (G-CP), to solve the problem through optimization over a vector space. The G-CP has key properties for solving the problem with G-CP and for applications to orthogonality constraint stochastic/distributed optimization problems. A numerical experiment shows that G-CP strategy outperforms the standard strategy with a retraction [Absil-Mahony-Sepulchre, 08]. |
