Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size - Statistics > Machine LearningReport as inadecuate




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Abstract: Independent component analysis ICA aims at decomposing an observed randomvector into statistically independent variables. Deflation-basedimplementations, such as the popular one-unit FastICA algorithm and itsvariants, extract the independent components one after another. A novel methodfor deflationary ICA, referred to as RobustICA, is put forward in this paper.This simple technique consists of performing exact line search optimization ofthe kurtosis contrast function. The step size leading to the global maximum ofthe contrast along the search direction is found among the roots of afourth-degree polynomial. This polynomial rooting can be performedalgebraically, and thus at low cost, at each iteration. Among other practicalbenefits, RobustICA can avoid prewhitening and deals with real- andcomplex-valued mixtures of possibly noncircular sources alike. The absence ofprewhitening improves asymptotic performance. The algorithm is robust to localextrema and shows a very high convergence speed in terms of the computationalcost required to reach a given source extraction quality, particularly forshort data records. These features are demonstrated by a comparative numericalanalysis on synthetic data. RobustICA-s capabilities in processing real-worlddata involving noncircular complex strongly super-Gaussian sources areillustrated by the biomedical problem of atrial activity AA extraction inatrial fibrillation AF electrocardiograms ECGs, where it outperforms analternative ICA-based technique.



Author: Vicente Zarzoso, Pierre Comon

Source: https://arxiv.org/







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