title: The fastICA algorithm revisited: convergence analysis.
abstract: The fast independent component analysis (FastICA) algorithm is one of the most popular methods to solve problems in ICA and blind source separation. It has been shown experimentally that it outperforms most of the commonly used ICA algorithms in convergence speed. A rigorous local convergence analysis has been presented only for the so-called one-unit case, in which just one of the rows of the separating matrix is considered. However, in the FastICA algorithm, there is also an explicit normalization step, and it may be questioned whether the extra rotation caused by the normalization will affect the convergence speed. The purpose of this paper is to show that this is not the case and the good convergence properties of the one-unit case are also shared by the full algorithm with symmetrical normalization. A local convergence analysis is given for the general case, and the global behavior is illustrated numerically for two sources and two mixtures in several typical cases.
authors.affiliation: Adaptive Informatics Research Centre, Helsinki University of Technology, 02015 HUT, Finland. erkki.oja@hut.fi
authors.forename: Erkki
authors.initials: E
authors.lastname: Oja
authors.forename: Zhijian
authors.initials: Z
authors.lastname: Yuan
mesh_terms: D000465:Algorithms; D016247:Information Storage and Retrieval / Q000379:methods*; D007257:Information Theory; D016571:Neural Networks, Computer; D010363:Pattern Recognition, Automated / Q000379:methods*; D025341:Principal Component Analysis