Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Machine Learning
Independent component analysis: algorithms and applications
Neural Networks
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Injecting noise for analysing the stability of ICA components
Signal Processing - Special issue on independent components analysis and beyond
Nonlinear Optimization
Support Vector Machines
Arabica: Robust ICA in a Pipeline
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
IEEE Transactions on Signal Processing
Fast and robust fixed-point algorithms for independent component analysis
IEEE Transactions on Neural Networks
The FastICA Algorithm Revisited: Convergence Analysis
IEEE Transactions on Neural Networks
Distributional convergence of subspace estimates in FastICA: a bootstrap study
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
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Independent component analysis (ICA) is possibly the most widespread approach to solve the blind source separation problem. Many different algorithms have been proposed, together with several highly successful applications. There is also an extensive body of work on the theoretical foundations and limits of the ICA methodology. One practical concern about the use of ICA with real world data is the robustness of its estimates. Slight variations in the estimates, may stem from the inherent stochastic nature of the algorithms used or some deviations from the theoretical assumptions. To overcome this problem, different approaches have been proposed, most of which are based on the use of multiple runs of ICA algorithms with bootstrap. Here we show the consistency and asymptotic normality of FastICA and bootstrap FastICA, based on empirical process theory, including Z-estimators and Hoeffding's inequality. These results give theoretical grounds for the robust use of FastICA, in a multiple run, bootstrap and randomly initialized manner. In this framework, it is also possible to assess the convergence of the algorithm through a normality test.