Name
Title | ||
|---|---|---|
A comparison of two algorithmic recipes to parametrize rectangular orthogonal matrices |
Abstract | ||
|---|---|---|
The present contribution focuses on the parametrization of rectangular (`tall-skinny') orthogonal matrices, which play a fundamental role in signal processing and machine learning. Such matrices form a smooth curved space termed compact Stiefel manifold. The present contribution aims at illustrating a numerical comparison of two algorithmic recipes to parameterize Stiefel matrices in signal processing. A closed-form algorithmic recipe was recently presented in the paper S. Fiori, T. Kaneko and T. Tanaka, “Learning on the compact Stiefel manifold by a Cayley-transform-based pseudo-retraction map,” in Proceedings of the 2012 International Joint Conference on Neural Networks (WCCI-IJCNN 2012, Brisbane (Australia), June 10 - 15, 2012), pp. 3434 - 3441, 2012, while a closed-form recipe was presented in the paper G.-X. Huang, F. Yin and K. Guo, “An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation A×B = C,” Journal of Computational and Applied Mathematics, Vol. 212, pp. 231 - 244, 2008. The numerical comparison shows that closed-form solution is substantially lighter than the iterative solution in terms of computational runtime, although the computational complexity of the closed-form solution grows slightly faster than the computational complexity of the iterative solution. |
Year | Venue | Keywords |
|---|---|---|
2012 | Signal & Information Processing Association Annual Summit and Conference | computational complexity,matrix algebra,Stiefel matrix parametrization,closed-form algorithmic recipe,compact Stiefel manifold,computational complexity,machine learning,rectangular orthogonal matrix parametrization,signal processing,smooth curved space,Averaging on differentiable manifolds,Cayley transform,Compact Stiefel manifold,Manifold pseudo-retraction and pseudo-lifting maps |
DocType | ISSN | ISBN |
Conference | 2309-9402 | 978-1-4673-4863-8 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simone Fiori | 1 | 494 | 52.86 |
| Tetsuya Kaneko | 2 | 0 | 0.34 |
| T. Tanaka | 3 | 638 | 95.91 |