Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
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
Arabica: Robust ICA in a Pipeline
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Subspaces of spatially varying independent components in fMRI
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Consistency and asymptotic normality of FastICA and bootstrap FastICA
Signal Processing
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
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Independent component analysis (ICA) is possibly the most widespread approach to solve the blind source separation (BSS) problem. Many different algorithms have been proposed, together with an extensive body of work on the theoretical foundations and limits of the methods. One practical concern about the use of ICA with real-world data is the reliability of its estimates. Variations of the estimates may stem from the inherent stochastic nature of the algorithm, or deviations from the theoretical assumptions. To overcome this problem, some approaches use bootstrapped estimates. The bootstrapping also allows identification of subspaces, since multiple separated components can share a common pattern of variation, when they belong to the same subspace. This is a desired ability, since real-world data often violates the strict independence assumption. Based on empirical process theory, it can be shown that FastICA and bootstrapped FastICA are consistent and asymptotically normal. In the context of subspace analysis, the normal convergence is not satisfied. This paper shows such limitation, and how to circumvent it, when one can estimate the canonical directions within the subspace.