Mathematics in independent component analysis

This paper intends to give an overview of the author's PhD thesis entitled 'mathematics in independent component analysis', which has been finished in December 2002.

[1]  Fabian J. Theis,et al.  Linear Geometric ICA: Fundamentals and Algorithms , 2003, Neural Computation.

[2]  Gilles Pagès,et al.  Two or three things that we know about the Kohonen algorithm , 1994, ESANN.

[3]  Fabian J. Theis,et al.  A Theoretical Framework for Overcomplete Geometric BMMR , 2002 .

[4]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[5]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[6]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[7]  Fabian J Theis,et al.  Formalization of the Two-Step Approach to Overcomplete BSS , 2002 .

[8]  Fabian J. Theis,et al.  FastGeo - A Histogram Based Approach to Linear Geometric ICA , 2001 .

[9]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[10]  A. J. Bell,et al.  INDEPENDENT COMPONENT ANALYSIS OF BIOMEDICAL SIGNALS , 2000 .

[11]  Michael Herrmann,et al.  Perspectives and limitations of self-organizing maps , 1996 .

[12]  B. Frieden,et al.  Image recovery: Theory and application , 1987, IEEE Journal of Quantum Electronics.

[13]  Fabian J. Theis,et al.  A geometric algorithm for overcomplete linear ICA , 2004, Neurocomputing.

[14]  E. Oja,et al.  Independent Component Analysis , 2013 .

[15]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[16]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[17]  Christian Jutten,et al.  Nonlinear source separation: the post-nonlinear mixtures , 1997, ESANN.

[18]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[19]  M. Cottrell,et al.  Etude d'un processus d'auto-organisation , 1987 .

[20]  Juha Karhunen,et al.  Local Linear Independent Component Analysis Based on Clustering , 2000, Int. J. Neural Syst..

[21]  Fabian J. Theis,et al.  Pattern Repulsion Revisited , 2001, IWANN.

[22]  Julio Ortega Lopera,et al.  Separation of sources: A geometry-based procedure for reconstruction of n-valued signals , 1995, Signal Process..

[23]  S. Sheather.  Density Estimation , 2004 .

[24]  Te-Won Lee,et al.  Nonlinear approaches to Independent Component Analysis , 2000 .

[25]  Juha Karhunen,et al.  A Maximum Likelihood Approach to Nonlinear Blind Source Separation , 1997, ICANN.

[26]  J. Nadal,et al.  Nonlinear neurons in the low-noise limit: a factorial code maximizes information transfer Network 5 , 1994 .

[27]  Carlos G. Puntonet,et al.  Neural net approach for blind separation of sources based on geometric properties , 1998, Neurocomputing.

[28]  Christian Jutten,et al.  Space or time adaptive signal processing by neural network models , 1987 .

[29]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Sub-Gaussian and Super-Gaussian Sources , 1999, Neural Comput..

[30]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[31]  Elmar Lang,et al.  Adaptive-geometric methods: Application to the separation of EEG signals , 2000 .

[32]  Fabian J. Theis,et al.  Nonlinear Geometric ICA , 2003 .

[33]  Teuvo Kohonen,et al.  Self-Organization and Associative Memory , 1988 .

[34]  Terrence J. Sejnowski,et al.  Blind source separation of more sources than mixtures using overcomplete representations , 1999, IEEE Signal Processing Letters.

[35]  Pierre Comon,et al.  Blind channel identification and extraction of more sources than sensors , 1998, Optics & Photonics.

[36]  Ralph Linsker,et al.  Local Synaptic Learning Rules Suffice to Maximize Mutual Information in a Linear Network , 1992, Neural Computation.

[37]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[38]  Neil Davey,et al.  Why will rat's go where rats will not? , 2002, ESANN.

[39]  Schuster,et al.  Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.

[40]  Fabian J. Theis,et al.  Overcomplete ICA with a Geometric Algorithm , 2002, ICANN.

[41]  Elmar Lang,et al.  Simulated annealing and density estimation for the separation of sources , 2000 .

[42]  Fabian J. Theis,et al.  Maximum Entropy and Minimal Mutual Information in a Nonlinear Model , 2001 .

[43]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[44]  Christian Jutten,et al.  Source separation in post-nonlinear mixtures , 1999, IEEE Trans. Signal Process..

[45]  A. Hyvarinen,et al.  On existence and uniqueness of solutions in nonlinear independent component analysis , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[46]  Te-Won Lee,et al.  Independent Component Analysis , 1998, Springer US.

[47]  Peter L. Bartlett,et al.  Neural Network Learning - Theoretical Foundations , 1999 .

[48]  Gilles Pagès,et al.  Convergence of the one-dimensional Kohonen algorithm , 1998, Advances in Applied Probability.

[49]  Ali Mansour,et al.  Separation of sources using simulated annealing and competitive learning , 2002, Neurocomputing.

[50]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[51]  B. De Moor,et al.  ICA algorithms for 3 sources and 2 sensors , 1999, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99.

[52]  H. Ritter,et al.  Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection , 1988, Biological Cybernetics.

[53]  Fabian J. Theis,et al.  How to generalize geometric ICA to higher dimensions , 2002, ESANN.

[54]  I︠u︡. V. Linnik,et al.  Decomposition of Random Variables and Vectors , 1977 .

[55]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[56]  Fabian J. Theis,et al.  Geometric overcomplete ICA , 2002, ESANN.

[57]  Christian Jutten,et al.  A geometric approach for separating post non-linear mixtures , 2002, 2002 11th European Signal Processing Conference.

[58]  Ralph Linsker,et al.  An Application of the Principle of Maximum Information Preservation to Linear Systems , 1988, NIPS.

[59]  A. Hyvärinen,et al.  Nonlinear Blind Source Separation by Self-Organizing Maps , 1996 .

[60]  Terrence J. Sejnowski,et al.  Learning Overcomplete Representations , 2000, Neural Computation.

[61]  Shun-ichi Amari,et al.  Adaptive Online Learning Algorithms for Blind Separation: Maximum Entropy and Minimum Mutual Information , 1997, Neural Computation.

[62]  W. Burnside.  Theory of Functions of a Complex Variable , 1893, Nature.

[63]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[64]  Fabian J. Theis,et al.  A HISTOGRAM-BASED OVERCOMPLETE ICA ALGORITHM , 2003 .

[65]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[66]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[67]  E. Lukács,et al.  A Property of the Normal Distribution , 1954 .

[68]  Fabian J. Theis,et al.  Extending Geometric ICA to Overcomplete and High-Dimensional BSS-Problems , 2002 .

[69]  David J. Field,et al.  Sparse Coding of Natural Images Produces Localized, Oriented, Bandpass Receptive Fields , 1995 .

[70]  Fabian J. Theis,et al.  Comparison of maximum entropy and minimal mutual information in a nonlinear setting , 2002, Signal Process..

[71]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[72]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[73]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[74]  H. P..  Annales de l'Institut Henri Poincaré , 1931, Nature.

[75]  Alberto Prieto,et al.  Separation of Speech Signals for Nonlinear Mixtures , 1999, IWANN.

[76]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[77]  B. Olshausen.  Learning linear, sparse, factorial codes , 1996 .

[78]  R W Prager,et al.  Development of low entropy coding in a recurrent network. , 1996, Network.