Learning averages over the lie group of unitary matrices

Authors:
Simone Fiori
Affiliations:
Dipartimento di Ingegneria Biomedica, Elettronica e Telecomunicazioni, Facoltà di Ingegneria, Università Politecnica delle Marche, Ancona, Italy
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

Citing 7
Cited 0

Compututational Techniques for Real Logarithms of Matrices

SIAM Journal on Matrix Analysis and Applications
Uniqueness of complex and multidimensional independent component analysis

Signal Processing
The Scaling and Squaring Method for the Matrix Exponential Revisited

SIAM Journal on Matrix Analysis and Applications
Nonlinear Complex-Valued Extensions of Hebbian Learning: An Essay

Neural Computation
A study on neural learning on manifold foliations: The case of the lie group su(3)

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

Neurocomputing
Equivariant adaptive source separation

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the present paper, we treat the problem of learning averages out of a set of unitary matrices. We discuss a possible learning technique based on the differential geometrical properties of the Lie group of unitary matrices. We first recall some relevant notions from differential geometry, mainly related to Lie group theory, and then we propose a scheme for learning averages. Some numerical experiments will illustrate the features of the learnt averages.