Leap-frog-type learning algorithms over the Lie group of unitary matrices

Authors:
Simone Fiori
Affiliations:
Dipartimento di Elettronica, Intelligenza Artificiale e Telecomunicazioni (DEIT), Facoltí di Ingegneria, Universití Politecnica delle Marche Via Brecce Bianche, Ancona I-60131, Italy
Venue:
Neurocomputing
Year:
2008

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Abstract

The aim of this paper is to discuss the class of leap-frog-type neural learning algorithms having the unitary group of matrices as parameter space. In the discussed framework, each step of a learning algorithm computes as an unconstrained learning step followed by a projection step. The present manuscript focuses on projection methods and related implementation issues. Projection methods based on singular/eigenvalue matrix decomposition as well as on QR decomposition are discussed in details. Two possible ways to combine these projection methods, based on projection-operator composition and on geodesic mid-point interpolation, are also discussed and tested numerically.