Paris' Independent Component Analysis & Blind Source Separation page

Independent Component Analysis (ICA) and Blind Source Separation (BSS) have received quite a lot of attention lately so that I decided to compile a list of online resources for whoever is interested. By no means is this page complete and if you have any additions do send me mail at paris at media dot mit dot edu. In the papers section I do not list all of the papers of every author (that's why you should check their homepages) but the really good ones are here. Also not all ICA & BSS people have home pages so if you discover any or if I missed yours tell me about it and I'll add them. Also note that this is a pretty ancient page, so expect many links to not work!
 

People working on ICA & BSS

• Pierre Comon, one of the first people to look at ICA, at the Laboratoire I3S of Universit? de Nice - Sophia Antipolis

• Tony Bell at the Salk Institute's Computational Neurobiology Lab

• Shun-ichi Amari at RIKEN's Lab for Information Synthesis

• Andrzej Cichocki at RIKEN's Laboratory for Open Information Systems

• Wlodzimierz Kasprzak at RIKEN's Laboratory for Open Information Systems

• Kari Torkkola at Motorola

• Erkki Oja at Helsinki University of Technology Laboratory of Computer and Information Science

• Juha Karhunen at Helsinki University of Technology Laboratory of Computer and Information Science

• Aapo Hyvarinen at Helsinki University of Technology Laboratory of Computer and Information Science

• Jean-Franηois Cardoso at the Ecole Nationale Supιrieure des Tιlιcommunications Signal Department

• Barak Pearlmutter at the University of New Mexico CS Department

• Mark Girolami at the University of Paisley Department of Computing and Information Systems
  (Looking for students)

• Te-Won Lee at the Salk Institute's Computational Neurobiology Lab

• Adel Belouchrani at Villanova University's Department of Electrical and Computer Engineering

• Simon Godsill and Dominic Chan at the Signal Processing and Communications Group at Cambridge University

• Juergen Schmidhuber at IDSIA

• Henrik Sahlin at Chalmers University of Technology.

• Seungjin Choi at Pohang University of Science and Technology.

• Gustavo Deco at Siemens.

• Hans van Hateren at the University of Groningen.

• Daniλl Schobben formerly at the Eindhoven University of Technology now at Phillips

• Vicente Zarzoso at the University of Strathclyde

• Kevin Knuth at the Albert Einstein College of Medicine

• Russ Lambert doing very cool things with sTrAnGe matrices!

• Alex Westner a brave man who scoffs at the complexity of real-world mixtures

• Daniel Rowe at Medical College of Wisconsin, doing Bayesian BSS

• Michael Zibulevsky at the University of New Mexico

• Na Kyungmin at the Seoul National University

• Lieven De Lathauwer at the Katholieke Universiteit Leuven

• Scott Rickard at Princeton

• Lucas Parra at the Sarnoff Corp.

• Simone Fiori at the Perugia University

• Carlos G. Puntonet at the University of Granada

• Andreas Ziehe at GMD FIRST

• Fathi Salam at the Circuits, Systems and Artificial Neural Networks Laboratory, Michigan State University

• Dinh-Tuan Pham at the Laboratoire de modelisation et calcul of IMAG

• Ali Mansour at the Ecole Nationale Supιrieure des Ingιnieurs des Etudes et Techniques d'Armement (ENSIETA)

• Ali Mohammad-Djafari at the Ecole superieure d'Electricitee (Supelec)

Other ICA Pages

• Te-Won Lee's ICA-CNL Page.

• Allan Barros' ICA Page.

• Tony Bell's ICA Page.

• Daniel Rowe's Bayesian BSS Page.

Benchmarks

• Daniλl Schobben, Kari Torkkola and me maintain these:
• Real world benchmarks
• Synthetic benchmarks

Code and Software ...

• Code from Pierre Comon.

• The FastICA package by Aapo Hyvδrinen (very cool, get it!)

• OOLABSS by Cichocki and Orsier.

• By Tony Bell, Here

• By Jean-Franηois Cardoso:
• The EASI Algorithm.
• The JADE Algorithm (and its calling program).

• By Dominic Chan, Here

• RICA by Cichocki and Barros.

• Genie by Na Kyungmin.

• By me:
• Mostly old instantaneous ICA code (in MATLAB)

Online Demos of BSS

• Barak Pearlmutter's Demo on Contextual ICA

• Te-Won Lee's Demo

• Dominic Chan's Demo

• My little frequency domain algorithm: (This is actually a static mix, I just put it up cause it sounds cool, but the algorithm can deal with convolved mixtures too)
• The input sound.
• The speech output (and in slow motion)
• The noise output (and in slow motion)

• Henrik Sahlin's demo.

• Hans van Hateren's demo on images.

• Daniλl Schobben's demo page

• Shiro Ikeda's demos

• Alex Westner's demos

• Scott Rickard's demo page

• Christian Jutten's JAVA demo

Online Papers on ICA & BSS

• Yes, I actually finished my dissertation!
• Smaragdis, P. 2001. Redundancy reduction for computational audition, a unifying approach. Ph.D. dissertation, MAS department, Massachusetts Institute of Technology.



• Smaragdis, P. 1997. Information Theoretic Approaches to Source Separation, Masters Thesis, MAS Department, Massachusetts Institute of Technology.
I realize that the name of the thesis is not terribly enlightening. What happens in there, apart from the obligatory background stuff, is the development of a new frequency domain separation algorithm to deal with convolved mixtures. The idea is to move to a space where the separation parameters are orthogonal, to assist convergence, and to be able to implement at the same time faster convolution schemes. In addition to this the algorithm is on-line and real-time so that you can actually use it. Results are nice too!
• Smaragdis, P. 1997. Efficient Blind Separation of Convolved Sound Mixtures,IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics. New Paltz NY, October 1997.
Pretty much the same material, geared towards DSP-heads. Written before my thesis so it is a little outdated.
• Smaragdis, P. 1998. Blind Separation of Convolved Mixtures in the Frequency Domain. International Workshop on Independence & Artificial Neural Networks University of La Laguna, Tenerife, Spain, February 9 - 10, 1998.
Condenced version of my thesis. Most up to date compared to my other offerings.

• Tony Bell has some neat papers on Blind Source Separation:
• Bell A.J. & Sejnowski T.J. 1995. An information-maximization approach to blind separation and blind deconvolution, Neural Computation, 7, 1129-1159.
• Bell A.J. & Sejnowski T.J. 1995. Fast blind separation based on information theory, in Proc. Intern. Symp. on Nonlinear Theory and Applications, vol. 1, 43-47, Las Vegas, Dec. 1995
And a couple of papers on ICA alone:
• Bell A.J. & Sejnowski T.J. 1996. Learning the higher-order structure of a natural sound, Network: Computation in Neural Systems, to appear
• Bell A.J. & Sejnowski T.J. 1996. The `Independent Components' of natural scenes are edge filters, Vision Research, under review [Please note that this is a draft].

• Kari Torkkola has some practical papers on simultaneous Blind Source Separation and Deconvolution:
• Torkkola, K.:Blind Separation of Delayed Sources Based on Information Maximization. Proceedings of the IEEE Conference on Acoustics, Speech and Signal Processing, May 7-10 1996, Atlanta, GA, USA.
• Torkkola, K.:Blind Separation of Convolved Sources Based on Information Maximization. IEEE Workshop on Neural Networks for Signal Processing, Sept 4-6 1996, Kyoto, Japan.
• Torkkola, K.:IIR Filters for Blind Deconvolution Using Information Maximizationrm. NIPS96 Workshop: Blind Signal Processing and Their Applications, Snowmaas (Aspen), Colorado.

• Barak Pearlmutter has a paper on context sensitive ICA:
• Barak A. Pearlmutter and Lucas C. Parra. A context-sensitive generalization of ICA. 1996 International Conference on Neural Information Processing. September 1996, Hong Kong.

• Erkki Oja has papers on PCA, nonlinear PCA and ICA:
• Oja, E., Karhunen, J., Wang, L., and Vigario, R.:Principal and independent components in neural networks - recent developments. Proc. VII Italian Workshop on Neural Nets WIRN'95, May 18 - 20, 1995, Vietri sul Mare, Italy (1995).
• Oja, E.:The nonlinear PCA learning rule and signal separation - mathematical analysis. Helsinki University of Technology, Laboratory of Computer and Information Science, Report A26 (1995).
• Oja, E. and Taipale, O.:Applications of learning and intelligent systems - the Finnish technology programme. Proc. Int. Conf. on Artificial Neural Networks ICANN-95, Industrial Conference, Oct. 9 - 13, 1995, Paris, France (1995).
• Oja, E.: PCA, ICA, and nonlinear Hebbian learning. Proc. Int. Conf. on Artificial Neural Networks ICANN-95, Oct. 9 - 13, 1995, Paris, France, pp. 89 - 94 (1995).
• Oja, E. and Karhunen, J.:Signal separation by nonlinear Hebbian learning. In M. Palaniswami, Y. Attikiouzel, R. Marks II, D. Fogel, and T. Fukuda (Eds.), Computational Intelligence - a Dynamic System Perspective. New York: IEEE Press, pp. 83 - 97 (1995).

• Juha Karhunen has written ICA & BSS papers with Oja (right above) and some on his own:
• Karhunen, J.:Neural Approaches to Independent Component Analysis and Source Separation. To appear in Proc. 4th European Symposium on Artificial Neural Networks (ESANN'96), April 24 - 26, 1996, Bruges, Belgium (invited paper).
• Karhunen, J., Wang, L., and Vigario, R.,Nonlinear PCA Type Approaches for Source Separation and Independent Component AnalysisProc. of the 1995 IEEE Int. Conf. on Neural Networks (ICNN'95), Perth, Australia, November 27 - December 1, 1995, pp. 995-1000.
• Karhunen, J., Wang, L., and Joutsensalo, J.,Neural Estimation of Basis Vectors in Independent Component Analysis Proc. of the Int. Conf. on Artificial Neural Networks (ICANN'95), Paris, France, October 9-13, 1995, pp. 317-322.

• Andrzej Cichocki organized a special invited session on BSS in Nolta '95 and has a nice list of papers on the subject:
(another apparently defunct set of links ...)
• Shun-ichi Amari, Andrzej Cichocki and Howard Hua Yang, "Recurrent Neural Networks for Blind Separation of Sources", , pp.37-42.
• Anthony J. Bell and Terrence J. Sejnowski, "Fast Blind Separation based on Information Theory", pp. 43-47.
• Adel Belouchrani and Jean-Francois Cardoso, "Maximum Likelihood Source Separation by the Expectation-Maximization Technique: Deterministic and Stochastic Implementation", pp.49-53.
• Jean-Francois Cardoso, "The Invariant Approach to Source Separation", pp. 55-60.
• Andrzej Cichocki, Wlodzimierz Kasprzak and Shun-ichi Amari, "Multi-Layer Neural Networks with Local Adaptive Learning Rules for Blind Separation of Source Signals", , pp.61-65.
• Yannick Deville and Laurence Andry, "Application of Blind Source Separation Techniques to Multi-Tag Contactless Identification Systems", , pp. 73-78.
• Jie Huang , Noboru Ohnishi and Naboru Sugie "Sound SeparatioN Based on Perceptual Grouping of Sound Segments", , pp.67-72.
• Christian Jutten and Jean-Francois Cardoso, "Separation of Sources: Really Blind ?" , pp. 79-84.
• Kiyotoshi Matsuoka and Mitsuru Kawamoto, "Blind Signal Separation Based on a Mutual Information Criterion", pp. 85-91.
• Lieven De Lathauwer, Pierre Comon, Bart De Moor and Joos Vandewalle, "Higher-Order Power Method - Application in Independent Component Analysis" , pp. 91-96.
• Jie Zhu, Xi-Ren Cao, and Ruey-Wen Liu, "Blind Source Separation Based on Output Independence - Theory and Implementation" , pp. 97-102.

Papers are included in Proceedings 1995 International Symposium on Nonlinear Theory and Applications NOLTA'95, Vol.1, NTA Research Society of IEICE, Tokyo, Japan, 1995.

• Shun-ichi Amari wrote some excelent papers with the RIKEN people on BSS and the math behind it:
• S. Amari, A. Cichocki and H. H. Yang, A New Learning Algorithm for Blind Signal Separation (128K), In: Advances in Neural Information Processing Systems 8, Editors D. Touretzky, M. Mozer, and M. Hasselmo, pp.?-?(to appear), MIT Press, Cambridge MA, 1996.
• Shun-ichi Amari, Neural Learning in Structured Parameter Spaces , NIPS'96
• Shun-ichi Amari, Information Geometry of Neural Networks - New Bayesian Duality Theory - , ICONIP'96
• Shun-ichi Amari, Gradient Learning in Structured Parameter Spaces: Adaptive Blind Separation of Signal Sources , WCNN'96
• Shun-ichi Amari and Jean-Francois Cardoso, Blind Source Separation - Semiparametric Statistical Approach, sumitted to IEEE Tr. on Signal Processing.
• Shun-ichi Amari, Natural Gradient Works Efficiently in Learning, sumitted to Neural Computation.
• Howard Hua Yang and Shun-ichi Amari, Adaptive On-Line Learning Algorithms for Blind Separation - Maximum Entropy and Minimum Mutual Information , accepted for Neural Computation.
• Shun-ichi Amari, Tian-Ping CHEN, Andrzej CICHOCKI, Stability Analysis of Adaptive Blind Source Separation , accepted for Neural Neworks.
• Shun-ichi Amari, Superefficiency in Blind Source Separation , sumitted to IEEE Tr. on Signal Processing.
• Shun-ichi Amari and Noboru Murata, Statistical Analysis of Regularization Constant - From Bayes, MDL and NIC Points of View, International Work-Donf. on Artificial and Natural Neural Networks 97.
• Shun-ichi Amari, Geometry of Semiparametric Models and Applications , ISI'97

• Jean-Franηois Cardoso has lots (and lots, and lots, ...) of papers on BSS!
• Jean-Franηois Cardoso and Beate Laheld. Equivariant adaptive source separation. To appear in IEEE Trans. on S.P.
• Jean-Franηois Cardoso. Performance and implementation of invariant source separation algorithms In Proc. ISCAS'96, 1996.
• Jean-Franηois Cardoso, Sandip Bose, and Benjamin Friedlander. On optimal source separation based on second and fourth order cumulants In Proc. IEEE Workshop on SSAP, Corfou, Greece, 1996.
• Jean-Franηois Cardoso. The equivariant approach to source separation In Proc. NOLTA, pages 55-60, 1995.
• Jean-Franηois Cardoso. Sιparation de sources dans l'espace signal In Proc. GRETSI, Juan les Pins,France, 1995.
• Jean-Franηois Cardoso. A tetradic decomposition of 4th-order tensors: application to the source separation problem In M. Moonen and B. de Moor, editors, Algorithms, architectures and applications, volume III of SVD and signal processing, pages 375-382. Elsevier, 1995.
• Jean-Franηois Cardoso, Sandip Bose, and Benjamin Friedlander. Output cumulant matching for source separation In Proc. IEEE SP Workshop on Higher-Order Stat., Aiguablava, Spain, pages 44-48, 1995.
• Adel Belouchrani and Jean-Franηois Cardoso. Maximum likelihood source separation for discrete sources In Proc. EUSIPCO, pages 768-771, Edinburgh, September 1994.
• Jean-Franηois Cardoso. On the performance of source separation algorithms In Proc. EUSIPCO, pages 776-779, Edinburgh, September 1994.
• Jean-Franηois Cardoso, Adel Belouchrani, and Beate Laheld. A new composite criterion for adaptive and iterative blind source separation In Proc. ICASSP, volume 4, pages 273-276, April 1994.
• Beate Laheld and Jean-Franηois Cardoso. Adaptive source separation with uniform performance In Proc. EUSIPCO, pages 183-186, Edinburgh, September 1994.
• Jean-Franηois Cardoso and Antoine Souloumiac. An efficient technique for blind separation of complex sources In Proc. IEEE SP Workshop on Higher-Order Stat., Lake Tahoe, USA, pages 275-279, 1993.
• Jean-Franηois Cardoso. Iterative techniques for blind source separation using only fourth order cumulants In Proc. EUSIPCO, pages 739-742, 1992.
• Jean-Franηois Cardoso and Beate Laheld. Adaptive blind source separation for channel spatial equalization In Proc. of COST 229 workshop on adaptive signal processing, pages 19-26, 1992.
• Jean-Franηois Cardoso. Eigen-structure of the fourth-order cumulant tensor with application to the blind source separation problem In Proc. ICASSP, pages 2655-2658, 1990.
• Jean-Franηois Cardoso. Source separation using higher order moments In Proc. ICASSP, pages 2109-2112, 1989.
• Jean-Franηois Cardoso and Pierre Comon. Independent component analysis, a survey of some algebraic methods In Proc. ISCAS'96, vol.2, pp. 93-96, 1996.
• Jean-Franηois Cardoso, Infomax and maximum likelihood for source separation,. To appear in IEEE Letters on Signal Processing, April, 1997.

• Cichocki & Kasprzak have a nice collection of papers:
• Cichocki A., Kasprzak W.: Nonlinear Learning Algorithms for Blind Separation of Natural Images , Neural Network World, vol.6, 1996, No.4, IDG Co., Prague, 515-523.
• Cichocki A., Kasprzak W., Amari S.-I.: Neural Network Approach to Blind Separation And Enhancement of Images , EUSIPCO'96 , (Trieste, Italy, September 1996).
• Kasprzak W., Cichocki A.: Hidden Image Separation From Incomplete Image Mixtures by Independent Component Analysis , ICPR'96 , Vienna, August 1996.
• Cichocki A., Amari S., Adachi M., Kasprzak W.: Self-Adaptive Neural Networks for Blind Separation of Sources , 1996 IEEE International Symposium on Circuits and Systems, ISCAS'96, Vol. 2, IEEE, Piscataway, NJ, 1996, 157-160.

• Mark Girolami at University of Paisley has some papers too:
• Girolami, M and Fyfe, C. Blind Separation of Sources Using Exploratory Projection Pursuit Networks. Speech and Signal Processing, International Conference on the Engineering Applications of Neural Networks, ISBN 952-90-7517-0, London, pp249-252, 1996.
• Girolami, M and Fyfe, C. Higher Order Cumulant Maximisation Using Nonlinear Hebbian and Anti-Hebbian Learning for Adaptive Blind Separation of Source Signals, Proc IWSIP-96, IEEE/IEE International Workshop on Signal and Image Processing, Advances in Computational Intelligence, Elsevier Science, pp141 - 144, Manchester, 4-7 November 1996.
• Girolami, M and Fyfe, C. Multivariate Density Factorisation for Independent Component Analysis : An Unsupervised Artificial Neural Network Approach, AISTATS-97, 3'rd International Workshop on Artificial Intelligence and Statistics, Fort Lauderdale, Florida, Jan 1997.
• Girolami, M and Fyfe, C. Negentropy and Kurtosis as Projection Pursuit Indices Provide Generalised ICA Algorithms, NIPS-96 Blind Signal Separation Workshop, (Org A. Cichocki & A.Back), Aspen, Colorado, 7 Dec, 1996.
• Girolami, M and Fyfe, C. A Temporal Model of Linear Anti-Hebbian Learning, Neural Processing Letters, In Press Vol 4, Issue 3, Jan 1997.

• Te-Won Lee at the Salk Institute has some interesting papers:
• Blind separation of delayed and convolved sources, T.W. Lee and A.J. Bell and R. Lambert, accepted for publication in "Advances in Neural Information Processing Systems", MIT Press, Cambridge MA, 1996
• Blind Source Separation of Real World Signals, T.W. Lee, A.J. Bell and R. Orglmeister, to appear in "IEEE International Conference Neural Networks ", Houston, 1997

• Aapo Hyvarinen has a nice bunch of papers:
• A. Hyvärinen. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 10(3):626-634, 1999.
• A. Hyvärinen and E. Oja. A Fast Fixed-Point Algorithm for Independent Component Analysis. Neural Computation, 9(7):1483-1492, 1997.
• A. Hyvärinen. New Approximations of Differential Entropy for Independent Component Analysis and Projection Pursuit. In Advances in Neural Information Processing Systems 10 (NIPS*97), pp. 273-279, MIT Press, 1998.

• Juergen Schmidhuber at IDSIA has related papers:
• S. Hochreiter and J. Schmidhuber. LOCOCODE. TR FKI-222-97, June 1997.
• J. Schmidhuber and M. Eldracher and B. Foltin. Semilinear predictability minimzation produces well-known feature detectors. Neural Computation, 8(4):773-786, 1996.
• J. Schmidhuber and D. Prelinger. Discovering predictable classifications. Neural Computation, 5(4):625-635, 1993.
• J. Schmidhuber. Learning factorial codes by predictability minimization. Neural Computation, 4(6):863-879, 1992.

• Henrik Sahlin's papers on separation and second order statistics:
• H. Broman, U. Lindgren, H. Sahlin and P. Stoica ``Source Separation: A TITO system identification approach'', Tech. rep. CTH-TE-33, Department of Applied Electronics, Chalmers University of Technology, Sept. 1995, Submitted to IEEE Trans. SP.
• H. Sahlin and U. Lindgren "The Asymptotic Cramer-Rao Lower Bound for Blind Signal Separation". "The Proceedings of the 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing", Corfu, Greece, 1996
• H. Sahlin "Asymptotic parameter variance analysis for Blind Signal Separation" "The proceedings of RVK96", Lulea, Sweden, 1996
• H. Sahlin and H. Broman "Blind Separation of Images" "The Proceedings of Asilomar Conference on Signals, Systems, and Computers", Pacific Grove, CA, USA, 1996.
• U. Lindgren, H. Sahlin and H. Broman "Source separation using second order statistics" "The Proceedings of EUSIPCO-96", Trieste, Italy, 1996.
• H. Sahlin, U. Lindgren and H. Broman "Multi Input Multi Output Blind Signal Separation Using Second Order Statistics" Tech. rep. CTH-TE-54, Department of Applied Electronics, Chalmers University of Technology, Dec., 1996.
• H. Sahlin "On Signal Separation by Second Order Statistics" Licentiate Thesis, Technical Report No. 251L, Department of Applied Electronics, Chalmers University of Technology, 1997.
• H. Sahlin and H. Broman "Signal Separation Applied to Real World Signals" Proceedings of International Workshop on Accoustic Echo and Noise Control, London, UK, September,1997.

• Gustavo Deco and Dragan Obradovic have an excellent book on ICA and related matters:
• An Information-Theoretic Approach to Neural Computing
• Second link

• Kevin Knuth on ICA:
• Bayesian source separation and localization. To be published in: SPIE'98 Proceedings: Bayesian Inference for Inverse Problems, San Diego, July 1998.

[pdf 475K], [doc 500K].
• Knuth K.H. 1999. A Bayesian approach to source separation. In: J.-F. Cardoso, C. Jutten and P. Loubaton (eds.), Proceedings of the First International Workshop on Independent Component Analysis and Signal Separation: ICA'99, Aussios, France, Jan. 1999, pp. 283-288.
• Knuth K.H. and Vaughan H.G., Jr. 1998. Convergent Bayesian formulations of blind source separation and electromagnetic source estimation. Presented at the MaxEnt98 workshop in Munich, July 1998.

• Alex Westner has worked on real world experiments:
• Westner, Alex. (1999) Object-Based Audio Capture: Separating Acoustically-Mixed Sounds. M.S. Thesis, Massachusetts Institute of Technology
• Westner, Alex and V. Michael Bove, Jr. (1999) cBlind separation of real world audio signals using overdetermined mixtures. To appear in Proceedings of ICA'99, Jan. 11-15, Aussois, France

• Roberto Manduchi on ICA and textures:
• R. Manduchi, J. Portilla, "Independent Component Analysis of Textures", accepted for presentation at IEEE International Conference on Computer Vision, Kerkyra, Greece, September 1999

• Michael Zibulevsky:
• Zibulevsky, M. and Pearlmutter, B.A. "Blind Source Separation by Sparse Decomposition", Technical Report CS99-1, Computer Science Department, University of New Mexico.

• Lucas Parra:
• Lucas Parra, Clay Spence, "On-line convolutive source separation of non-stationary signals", Journal of VLSI Signal Processing, Special issue on the 1998 IEEE Neural Networks and Signal Processing Workshop, to appear in summer 2000, (.ps.gz 249K, .pdf 482K)
• Lucas Parra, Klaus-Robert Mueller, Clay Spence, Andreas Ziehe, Paul Sajda, "Unmixing Hyperspectral Data", Advances in Neural Information Processing Systems 12, MIT Press, to appear 1999. (.ps.gz 76K)

• Simone Fiori has some papers on ICA by the adaptive activation function networks and learning on Stiefel-Grassman manifold:
• S. Fiori, "Entropy Optimization by the PFANN Network: Application to Independent Component Analysis", Network: Computation in Neural Systems, Vol. 10, No. 2, pp. 171 - 186, May 1999
• S. Fiori, "'Mechanical' Neural Learning for Blind Source Separation", Electronics Letters, Vol. 35, No. 22, pp. 1963 - 1964, Oct. 1999
• S. Fiori, "Blind Separation of Circularly Distributed Source Signals by the Neural Extended APEX Algorithm", Neurocomputing, Vol. 34, No. 1-4, pp. 239 - 252, August 2000
• S. Fiori, "Blind Signal Processing by the Adaptive Activation Function Neurons", Neural Networks, Vol. 13, No. 6, pp. 597 - 611, August 2000
• S. Fiori, "A Theory for Learning by Weight Flow on Stiefel-Grassman Manifold", Neural Computation. Accepted for publication: To appear.