@article{bald88,
author="Pierre Baldi and Kurt Hornik",
title="Neural Networks and Principal Component Analysis: 
Learning from Examples Without Local Minima",
year=1989,
journal="Neural Networks",
volume=2,
number=1,
pages="53--58"}

@article{oja82,
author="Erkki Oja",
title="A Simplified Neuron Model as a Principal Component Analyzer",
journal="J. Math. Biology",
year=1982,
volume=15,
pages="267--273"}

@article{bour87,
author="H. Bourlard and Y. Kamp",
title="Auto-Association by Multilayer Perceptrons and Singular Value
			Decomposition",
year=1988,
journal="Biological Cybernetics",
volume=59,
pages="291--294"}

@inproceedings{owsl78,
	author="N. L. Owsley",
	title="Adaptive Data Orthogonalization",
	booktitle="{Proc. 1978 {IEEE} Int. Conf. on Acoustics, Speech,
		and Signal Processing, Tulsa OK}",
	month="April 10--12",
	publisher="{IEEE} Press",
	address="Piscataway, {NJ}",
	year=1978,
	pages="109--112"}

@article{oja85,
	author="Erkki Oja and Juha Karhunen",
	title="On Stochastic Approximation of the Eigenvectors and
		Eigenvalues of the Expectation of a Random Matrix",
	journal="J. Math. Analysis and Appl.",
	volume=106,
	pages="69--84",
	year=1985}

@book{oja83,
	author="Erkki Oja",
	title="Subspace Methods of Pattern Recognition",
	publisher="Research Studies Press",
	address="Letchworth, Hertfordshire UK",
	year=1983}

@inproceedings{karh84b,
	author="Juha Karhunen",
	title="Adaptive Algorithms for Estimating Eigenvectors of
		Correlation Type Matrices",
	booktitle="{Proc. 1984 {IEEE} Int. Conf. on Acoustics, Speech,
		and Signal Processing}",
	publisher="{IEEE} Press",
	address="Piscataway, {NJ}",
	year=1984,
	pages="14.6.1--14.6.4"}

@inproceedings{karh82,
	author="Juha Karhunen and Erkki Oja",
	title="New Methods for Stochastic Approximation of Truncated
		{Karhunen-Lo\`{e}ve} Expansions",
	booktitle="{Proc. 6th Int. Conf. on Pattern Recognition}",
	year=1982,
	publisher="{Springer}-{Verlag}",
	address="{NY}",
	month="October",
	pages="550--553"}

@inproceedings{oja80,
	author="Erkki Oja and Juha Karhunen",
	title="Recursive Construction of {Karhunen-Lo\`{e}ve} Expansions
		for Pattern Recognition Purposes",
	booktitle="{Proc. 5th Int. Conf. on Pattern Recognition}",
	publisher="Springer-{Verlag}",
	address="{NY}",
	year=1980,
	month="December",
	pages="1215--1218"}

@inproceedings{kuus82,
	author="Maija Kuusela and Erkki Oja",
	title="The Averaged Learning Subspace Method for Spectral
		Pattern Recognition",
	booktitle="{Proc. 6th Int. Conf. on Pattern Recognition}",
	year=1982,
	publisher="Springer-{Verlag}",
	address="{NY}",
	month="October",
	pages="134--137"}

@phdthesis{karh84,
	author="Juha Karhunen",
	title="Recursive Estimation of Eigenvectors of Correlation Type
		Matrices for Signal Processing Applications",
	school="Helsinki Univ. Tech.",
	year=1984,
	address="Espoo, Finland"}

@techreport{karh85,
	author="Juha Karhunen",
	title="Simple Gradient Type Algorithms for Data-Adaptive Eigenvector
		Estimation",
	institution="Helsinki Univ. Tech.",
	year=1985,
	number="TKK-F-A584"}


@article{sang89a,
	author="Terence David Sanger",
	title="Optimal Unsupervised Learning in a Single-Layer Linear
		Feedforward Neural Network",
	year=1989,
	journal="Neural Networks",
	volume=2,
	pages="459--473"}

@misc{sang89b,
	author="Terence David Sanger",
	title="Optimal Unsupervised Learning in Feedforward Neural Networks",
	year=1989,
	note="MIT AI Lab Tech. Report 1086"}

@incollection{sang89c,
	author="Terence David Sanger",
	title="An Optimality Principle for Unsupervised Learning",
	year=1989,
	pages="11--19",
	booktitle="Advances in Neural Information Processing
		Systems 1",
	editor="David S. Touretzky",
	publisher="Morgan Kaufmann",
	address="San Mateo, {CA}",
	note="Proc. {NIPS'88}, Denver"}

@inproceedings{broc89,
	author="Roger W. Brockett",
	title="Dynamical Systems that Sort Lists, Diagonalize Matrices,
		and Solve Linear Programming Problems",
        booktitle="Proc. 1988 {IEEE} Conference on Decision and Control",
        publisher="{IEEE}",
        address="New York",
        pages="799--803",
	year=1988}

@incollection{broc91,
  author = "Roger W. Brockett",
  title = "Dynamical Systems that Learn Subspaces",
  booktitle= "{Mathematical System Theory; the influence of R.E. Kalman}",
  editor = "Athanasios C. Antoulas",
  pages = "579--592",
  publisher = "Springer-Verlag",
  address = "New York",
  year = 1991
}

@article{sang90c,
	author="Terence D. Sanger",
	title="Optimal Hidden Units for Two-layer Nonlinear
               Feedforward Neural Networks",
	year=1991,
	journal="International Journal of Pattern Recognition and 
		Artificial Intelligence",
	volume=5,
	number=4,
	pages = "545--561",
	note="Also appears in C. H. Chen, ed., {\it Neural Networks in
		Pattern Recognition and Their Applications}, World
		Scientific, 1991, pp. 43-59"} 

@INCOLLECTION{krog90,
	AUTHOR = {Anders Krogh and John A. Hertz},
	TITLE = {Hebbian Learning of Principal Components},
	BOOKTITLE = {Parallel Processing in Neural Systems and Computers},
	PUBLISHER = {Elsevier Science Publishers B.V.},
	YEAR = {1990},
	EDITOR = {R. Eckmiller and G. Hartmann and G. Hauske},
	PAGES = {183--186},
	ADDRESS = {North-Holland}
}

@INPROCEEDINGS{fold89,
	AUTHOR = {Peter Foldiak},
	TITLE = {Adaptive Network for Optimal Linear Feature Extraction},
	BOOKTITLE = {Proc. {IJCNN}},
	YEAR = {1989},
	PAGES = {401--406},
	ORGANIZATION = {{IEEE/INNS}},
	ADDRESS = {Washington, D.C.},
	MONTH = {June}
}

@MISC{kung90,
	AUTHOR = {S. Y. Kung},
	TITLE = {Neural networks for Extracting Constrained Principal
		Components},
	YEAR = {1990},
	NOTE = {submitted to {\it IEEE Trans. Neural Networks}}
}

@ARTICLE{rubn90,
	AUTHOR = {J. Rubner and K. Schulten},
	TITLE = {Development of Feature Detectors by Self-Organization},
	JOURNAL = {Biological Cybernetics},
	YEAR = {1990},
	VOLUME = {62},
	PAGES = {193--199}
}

@article{rubn89,
author = "J. Rubner and P. Tavan",
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volume = 10,
number = 7,
pages = "693--698",
year = 1989}

@misc{ogaw86,
  author = "Hidemitsu Ogawa and Erkki Oja",
  title = "Can we Solve the Continuous Karhunen-Loeve Eigenproblem
           from Discrete Data?",
  note = "Proc. {IEEE} Eighth International Conference on Pattern Recognition,
          Paris",
  year = "1986"}

@incollection{silv91,
  author = "Fernando M. Silva and Luis B. Almeida",
  title = "A Distributed Decorrelation Algorithm",
  booktitle = "Neural Networks, Advances and Applications",
  editor = "Erol Gelenbe",
  publisher = "North-Holland",
  year = "1991",
  note = "to appear"}

@misc{bann93,
author = "S. Bannour and M. R. {Azimi-Sadjadi}",
title = "Principal Component Extraction using Recursive Least Squares
		 Learning",
year = 1993,
note = "submitted to {\it {IEEE} Transactions on Neural Networks}"}

@article{smit91,
author = "Steven T. Smith",
title = "Dynamical Systems that Perform the Singular Value Decomposition",
journal = "Systems and Control Letters",
volume = 16,
year = 1991,
pages = "319--327"}

@misc{fold92,
author = "Peter Foldiak",
title = "Models of Sensory Coding",
year = 1992,
note = "Physiological Laboratory, University of Cambridge
		 CUED/F-INFENG/TR91"}

@misc{xu91,
author = "Lei Xu",
title = "Least {MSE} Reconstruction:  A Principle for Self-Organizing
		 Neural-Nets?",
year = 1991,
note = "Peking Univ. Dept. Mathematics TR X9152"}

@misc{will85,
author = "Ronald J. Williams",
title = "Feature Discovery through Error-Correction Learning",
year = 1985,
month = "May",
note = "{UCSD} Institute for Cognitive Science Tech. Report 8501"}

@article{whit92,
author = "Ray H. White",
title = "Competitive Hebbian Learning:  Algorithms and Demonstrations",
journal = "Neural Networks",
volume = 5,
year = 1992,
pages = "261--275"}

@article{cich92,
author = "A. Cichocki and R. Unbehauen",
title = "Neural Networks for Computing Eigenvalues and Eigenvectors",
journal = "Biological Cybernetics",
year = 1992,
volume = 68,
pages = "155--164"}

@article{lenz92,
author = "Reiner Lenz and Mats Osterberg",
title = "Computing the Karhunen-Loeve Expansion with a Parallel,
		 Unsupervised Filter System",
journal = "Neural Computation",
year = 1992,
volume = 4,
pages = "382--392"}

@inproceedings{kung90,
author = "S. Y. Kung and K. I. Diamantaras",
title = "A Neural Network Learning Algorithm for Adaptive Principal
		 Component Extraction",

booktitle = "Proc. {IEEE} International Conf. on Acoustics Speech and
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address = "Albuquerque",
year = 1990,
pages = "861--864"}

@incollection{leen91,
author = "Todd Leen", 
title = "Dynamics of Learning in Recurrent Feature-Discovery Networks", 
editor = "R. Lippmann, J. Moody and D. Touretzky", 
booktitle = "Advances in Neural Information Processing Systems 3", 
publisher = "Morgan Kaufmann", 
year = 1991}

@article{amar77,
author = "S.Amari", 
title = "Neural Theory of Association and Concept Formation", 
journal = "Biological Cybernetics", 
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year = 1977}

@inproceedings{whit92b,
author = "Ray H. White",
title = "Recurrent Competitive Hebbian Learning",
year = 1992,
booktitle = "Proceedings IJCNN'92 - Baltimore",
volume = IV,
pages = "767-772"}

@inproceedings{whit93,
author = "Ray H. White",
title = "Competitive Hebbian Learning 2: an Introduction",
year = 1993,
booktitle = "Proceddings WCNN'93 - Portland",
volume = II,
pages = "557-571"}

@article{link92,
author = "Ralph Linsker",
title = "Local synaptic rules suffice to maximize mutual information
in a linear network",
journal = "Neural Computation",
volume = 4,
pages = "691-702",
year = 1992}

@article{xu93,
author = "L. Xu",
title = "Least mean square error reconstruction principle for
self-organizing neural-nets",
journal = "Neural Networks",
volume = 6,
pages ="627-648",
year = 1993}

@article{oja92a,
author = "E. Oja and H. Ogawa and J. Wangviwattana",
title =  "Principal component
analysis by homogeneous neural networks, Part {I}: The weighted
subspace criterion",
journal = " IEICE Trans. Inf. and Systems", 
volume =  "E75-D",
number =  3, 
month = "May",
year = 1992, 
pages =  "366 - 375"}

@article{oja92b,
author = "E. Oja, H. Ogawa and J. Wangviwattana",
title =  "Principal component
analysis by homogeneous neural networks, Part {II}: Analysis and 
extensions of the learning algorithms",
journal = " IEICE Trans. Inf. and Systems", 
volume =  "E75-D",
number =  3, 
month = "May",
year = 1992, 
pages = " 376 - 382"}

@article{oja92c,
author = "Erkki Oja",
title = "Principal Components, Minor Components, and Linear Neural
		 Networks",
journal = "Neural Networks",
volume = 5,
pages = "927--935",
year = 1992}

@techreport{oja93a,
author = "Erkki Oja and Juha Karhunen",
title = "Nonlinear {PCA}: Algorithms and Applications",
institution = "Helsinki University of Technology Laboratory of Computer and
		 Information Sciences",
number = "A18",
year = 1993,
month = "September",
address = "Rakentajanaukio 2 C, SF-02150 Espoo, Finland"}

@techreport{oja93b,
author = "Erkki Oja",
title = "A Nonlinear Symmetrical {PCA} Network Learns true Principal
		 Components",
institution = "Lappeenranta University of Technology, Department of
		 Information Technology",
number = "Research Report 40",
year = 1993,
address = "Box 20, SF-53851, Lappeenranta Finland"}

@incollection{bald94a,
author = "Pierre Baldi and Yves Chauvin and Kurt Hornik",
title = "Back-propagation and unsupervised learning in linear networks",
booktitle = "Back-propagation: Theory, Architectures and Applications",
editors = "Y. Chauvin and D.E. Rumelhart",
publisher = "Lawrence Erlbaum Associates",
year = 1994,
note = "In press"}

@misc{bald94b,
author = "Pierre Baldi and Kurt Hornik",
year = 1994",
title = "Learning in Linear Networks",
note = "Submitted"}