Topics in matrix analysis
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Complex independent component analysis of frequency-domain electroencephalographic data
Neural Networks - Special issue: Neuroinformatics
Local stability analysis of flexible independent component analysis algorithm
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 06
EURASIP Journal on Applied Signal Processing
Complex-valued adaptive signal processing using nonlinear functions
EURASIP Journal on Advances in Signal Processing
Probabilistic Formulation of Independent Vector Analysis Using Complex Gaussian Scale Mixtures
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
A complex generalized Gaussian distribution: characterization, generation, and estimation
IEEE Transactions on Signal Processing
Use of the Newton Method for Blind Adaptive Equalization Based on the Constant Modulus Algorithm
IEEE Transactions on Signal Processing - Part II
Blind separation of mixture of independent sources through aquasi-maximum likelihood approach
IEEE Transactions on Signal Processing
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
Complex ICA Using Nonlinear Functions
IEEE Transactions on Signal Processing
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
Stability of independent vector analysis
Signal Processing
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part I
Cramér-Rao bound for circular complex independent component analysis
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Hi-index | 35.68 |
We derive a class of algorithms for independent component analysis (ICA) based on maximum likelihood (ML) estimation and perform stability analysis of natural gradient ML ICA with and without the constraint for unitary demixing matrix. In the process, we demonstrate how Wirtinger calculus facilitates derivations, and most importantly, performing second-order analysis in the complex domain and eliminates the need for making simplifying assumptions. We derive natural gradient complex ML ICA update rule and its variant with a unitary constraint, as well as a Newton algorithm for better convergence behavior. The conditions for local stability are derived and studied using a generalized Gaussian density (GGD) source model. When the sources are circular and non-Gaussian, we show analytically that both the ML and ML-unitary ICA update rules converge to the inverse of mixing matrix subject to a phase shift. When the sources are noncircular and non-Gaussian, we show that the nonunitary ML ICA update rule is more stable than the ML-unitary ICA update rule. When the sources are noncircular Gaussians, both update rules are stable only when the sources have distinct noncircularity indices. Simulation results are given to support these results.