Mathematics in Independent Component Analysis

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174 Chapter 11. EURASIP JASP, 2007 Fabian J. Theis et al. 13 [19] M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation, vol. 13, no. 4, pp. 863–882, 2001. [20] F. J. Theis, P. Georgiev, and A. Cichocki, “Robust overcomplete matrix recovery for sparse sources using a generalized Hough transform,” in Proceedings of 12th European Symposium on Artificial Neural Networks (ESANN ’04), pp. 343–348, Bruges, Belgium, April 2004, d-side, Evere, Belgium. [21] P. S. Bradley and O. L. Mangasarian, “k-plane clustering,” Journal of Global Optimization, vol. 16, no. 1, pp. 23–32, 2000. [22] P. Georgiev, P. Pardalos, F. J. Theis, A. Cichocki, and H. Bakardjian, “Sparse component analysis: a new tool for data mining,” in Data Mining in Biomedicine, Springer, New York, NY, USA, 2005, in print. [23] P. Georgiev, F. J. Theis, and A. Cichocki, “Optimization algorithms for sparse representations and applications,” in Multiscale Optimization Methods, P. Pardalos, Ed., Springer, New York, NY, USA, 2005. [24] R. O. Duda and P. E. Hart, “Use of the Hough transformation to detect lines and curves in pictures,” Communications of the ACM, vol. 15, no. 1, pp. 204–208, 1972. [25] R. Dudley, Department of Mathematics, MIT, course 18.465, 2005. [26] P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection, John Wiley & Sons, New York, NY, USA, 1987. [27] P. Ballester, “Applications of the Hough transform,” in Astronomical Data Analysis Software and Systems III, J. Barnes, D. R. Crabtree, and R. J. Hanisch, Eds., vol. 61 of ASP Conference Series, 1994. [28] A. Goldenshluger and A. Zeevi, “The Hough transform estimator,” Annals of Statistics, vol. 32, no. 5, pp. 1908–1932, 2004. [29] A. Hyvärinen and E. Oja, “A fast fixed-point algorithm for independent component analysis,” Neural Computation, vol. 9, no. 7, pp. 1483–1492, 1997. [30] F. J. Theis and G. A. García, “On the use of sparse signal decomposition in the analysis of multi-channel surface electromyograms,” Signal Processing, vol. 86, no. 3, pp. 603–623, 2006. Fabian J. Theis obtained his M.S. degree in mathematics and physics from the University of Regensburg, Germany, in 2000. He also received the Ph.D. degree in physics from the same university in 2002 and the Ph.D. degree in computer science from the University of Granada in 2003. He worked as a Visiting Researcher at the Department of Architecture and Computer Technology (University of Granada, Spain), at the RIKEN Brain Science Institute (Wako, Japan), at FAMU-FSU (Florida State University, USA), and at TUAT’s Laboratory for Signal and Image Processing (Tokyo, Japan). Currently, he is heading the Signal Processing & Information Theory Group at the Institute of Biophysics at the University of Regensburg and is working on his habilitation. He serves as an Associate Editor of “Computational Intelligence and Neuroscience,” and is a Member of IEEE, EURASIP, and ENNS. His research interests include statistical signal processing, machine learning, blind source separation, and biomedical data analysis. Pando Georgiev received his M.S., Ph.D., and “Doctor of Mathematical Sciences” degrees in mathematics (operations research) from Sofia University “St. Kl. Ohridski,” Bulgaria, in 1982, 1987, and 2001, respectively. He has been with the Department of Probability, Operations Research, and Statistics at the Faculty of Mathematics and Informatics, Sofia University “St. Kl. Ohridski,” Bulgaria, as an Assistant Professor (1989–1994), and since 1994, as an Associate Professor. He was a Visiting Professor at the University of Rome II, Italy (CNR grants, several one-month visits), the International Center for Theoretical Physics, Trieste, Italy (ICTP grant, six months), the University of Pau, France (NATO grant, three months), Hirosaki University, Japan (JSPS grant, nine months), and so forth. He has been working for four years (2000–2004) as a research scientist at the Laboratory for Advanced Brain Signal Processing, Brain Science Institute, the Institute of Physical and Chemical Research (RIKEN), Wako, Japan. After that and currently he is a Visiting Scholar in ECECS Department, University of Cincinnati, USA. His interests include machine learning and computational intelligence, independent and sparse component analysis, blind signal separation, statistics and inverse problems, signal and image processing, optimization, and variational analysis. He is a Member of AMS, IEEE, and UBM. Andrzej Cichocki was born in Poland. He received the M.S. (with honors), Ph.D., and Habilitate Doctorate (Dr.Sc.) degrees, all in electrical engineering, from the Warsaw University of Technology (Poland) in 1972, 1975, and 1982, respectively. He is the coauthor of three international and successful books (two of them were translated to Chinese): Adaptive Blind Signal and Image Processing (John Wiley, 2002) MOS Switched- Capacitor and Continuous-Time Integrated Circuits and Systems (Springer, 1989), and Neural Networks for Optimization and Signal Processing (J. Wiley and Teubner Verlag, 1993/1994) and the author or coauthor of more than three hundred papers. He is the Editorin-Chief of the Journal Computational Intelligence and Neuroscience and an Associate Editor of IEEE Transactions on Neural Networks. Since 1997, he has been the Head of the Laboratory for Advanced Brain Signal Processing in the Riken Brain Science Institute, Japan.
Chapter 12 LNCS 3195:718-725, 2004 Paper F.J. Theis and S. Amari. Postnonlinear overcomplete blind source separation using sparse sources. In Proc. ICA 2004, volume 3195 of LNCS, pages 718- 725, Granada, Spain, 2004 Reference (Theis and Amari, 2004) Summary in section 1.4.1 175
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