A fast fixed-point algorithm for independent component analysis
Neural Computation
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
On a differential equation approach to the weighted orthogonal Procrustes problem
Statistics and Computing
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
On the convergence of ICA algorithms with symmetric orthogonalization
IEEE Transactions on Signal Processing
Local convergence analysis of FastICA
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Optimization algorithms exploiting unitary constraints
IEEE Transactions on Signal Processing
On gradient adaptation with unit-norm constraints
IEEE Transactions on Signal Processing
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Monotonic convergence of fixed-point algorithms for ICA
IEEE Transactions on Neural Networks
The FastICA Algorithm Revisited: Convergence Analysis
IEEE Transactions on Neural Networks
Adaptive weighted orthogonal constrained algorithm for blind source separation
Digital Signal Processing
| Hi-index | 0.00 |
A kind of weighted orthogonal constrained independent component analysis (ICA) algorithms with weighted orthogonalization for achieving this constraint is proposed recently. It has been proved in the literature that weighted orthogonal constrained ICA algorithms keep the equivariance property and have much better convergence speed, separation ability and steady state misadjustment, but the convergence is not yet analyzed in the published literature. The goal of this paper is to fill this gap. Firstly, a characterization of the stationary points corresponding to these algorithms using symmetric Minimum Distance Weighted Unitary Mapping (MDWUM) for achieving the weighted orthogonalization is obtained. Secondly, the monotonic convergence of the weighted orthogonal constrained fixed point ICA algorithms using symmetric MDWUM for convex contrast function is proved, which is further extended to nonconvex contrast functions case by adding a weighted orthogonal constraint term onto the contrast function. Together with the boundedness of contrast function, the convergence of fixed point ICA algorithms with weighted orthogonal constraint using symmetric MDWUM is implied. Simulation experiments results show that the adaptive ICA algorithms using symmetric MDWUM are better in terms of accuracy than the ones with pre-whitening, and the fixed-point ICA algorithms using symmetric MDWUM converge monotonically.