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LEARNING BY CRITERION OPTIMIZATION ON A UNITARY UNIMODULAR MATRIX GROUP

Authors :
Simone Fiori
Source :
International Journal of Neural Systems. 18:87-103
Publication Year :
2008
Publisher :
World Scientific Pub Co Pte Lt, 2008.

Abstract

The present manuscript aims at illustrating fundamental challenges and solutions arising in the design of learning theories by optimization on manifolds in the context of complex-valued neural systems. The special case of a unitary unimodular group of matrices is dealt with. The unitary unimodular group under analysis is a low dimensional and easy-to-handle matrix group. Notwithstanding, it exhibits a rich geometrical structure and gives rise to interesting speculations about methods to solve optimization problems on manifolds. Also, its low dimension allows us to treat most of the quantities involved in computation in closed form as well as to render them in graphical format. Some numerical experiments are presented and discussed within the paper, which deal with complex-valued independent component analysis.

Details

ISSN :
17936462 and 01290657
Volume :
18
Database :
OpenAIRE
Journal :
International Journal of Neural Systems
Accession number :
edsair.doi.dedup.....a5478d2019042ecc807a22d704ec1e0d
Full Text :
https://doi.org/10.1142/s0129065708001415