Conjugate gradient algorithm for optimization under unitary matrix constraint

Authors:
Traian Abrudan;Jan Eriksson;Visa Koivunen
Affiliations:
SMARAD CoE, Department of Signal Processing and Acoustics, Helsinki University of Technology, FIN-02015 HUT, Finland;SMARAD CoE, Department of Signal Processing and Acoustics, Helsinki University of Technology, FIN-02015 HUT, Finland;SMARAD CoE, Department of Signal Processing and Acoustics, Helsinki University of Technology, FIN-02015 HUT, Finland
Venue:
Signal Processing
Year:
2009

Citing 11
Cited 1

Geometric optimization methods for adaptive filtering

Geometric optimization methods for adaptive filtering
Optimization: algorithms and consistent approximations

Optimization: algorithms and consistent approximations
The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial

The Journal of Machine Learning Research
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
Descent methods for optimization on homogeneous manifolds

Mathematics and Computers in Simulation
Learning algorithms utilizing quasi-geodesic flows on the Stiefel manifold

Neurocomputing
Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras

Neurocomputing
Optimization algorithms exploiting unitary constraints

IEEE Transactions on Signal Processing
Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint

IEEE Transactions on Signal Processing

Brief paper: Non-parametric methods for L2-gain estimation using iterative experiments

Automatica (Journal of IFAC)

Quantified Score

Hi-index	0.08

Visualization

Abstract

In this paper we introduce a Riemannian algorithm for minimizing (or maximizing) a real-valued function J of complex-valued matrix argument W under the constraint that W is an nxn unitary matrix. This type of constrained optimization problem arises in many array and multi-channel signal processing applications. We propose a conjugate gradient (CG) algorithm on the Lie group of unitary matrices U(n). The algorithm fully exploits the group properties in order to reduce the computational cost. Two novel geodesic search methods exploiting the almost periodic nature of the cost function along geodesics on U(n) are introduced. We demonstrate the performance of the proposed CG algorithm in a blind signal separation application. Computer simulations show that the proposed algorithm outperforms other existing algorithms in terms of convergence speed and computational complexity.