Theis, Fabian J. and Jung, Andreas and Puntonet, Carlos G. and Lang, Elmar W. (2003) Linear Geometric ICA: Fundamentals and Algorithms. Neural Computation 15, pp. 419-439.
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Other URL: http://neco.mitpress.org/cgi/content/abstract/15/2/419?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&searchid=1105816667459_105&stored_search=&FIRSTINDEX=0&sortspec=relevance&volume=15&firstpage=419&journalcode=neco
Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (1995). We will reconsider geometric ICA in a theoretic framework showing that fixed points of geometric ICA fulfill a geometric convergence condition (GCC), which the mixed images of the unit vectors satisfy too. This leads to a conjecture claiming that in the nongaussian unimodal symmetric case, there is only one stable fixed point, implying the uniqueness of geometric ICA after convergence. Guided by the principles of ordinary geometric ICA, we then present a new approach to linear geometric ICA based on histograms observing a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost, by a factor of 100, compared to the ordinary geometric approach. Furthermore, we explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix, and compare geometric algorithms with classical ICA algorithms, namely, Extended Infomax and FastICA. Finally, we discuss the problem of high-dimensional data sets within the realm of geometrical ICA algorithms.
|Institutions:|| Biology, Preclinical Medicine > Institut für Biophysik und physikalische Biochemie > Prof. Dr. Elmar Lang|
Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter
|Projects:||Graduiertenkolleg Nichtlinearität und Nichtgleichgewicht|
|Subjects:||500 Science > 530 Physics|
500 Science > 570 Life sciences
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||20 Mar 2007|
|Last Modified:||20 Jul 2011 20:58|