Algorithms for Principal Components Analysis

Tue Nov 12 17:54:54 EST 1991

Ray,

Over the past few years there has been a great deal of interest in recursive
algorithms for finding eigenvectors or linear combinations of them.  Many
of these algorithms are based on the Oja rule (1982) with modifications to
find more than a single output.  As might be expected, so many people
working on a single type of algorithm has led to a certain amount of
duplication of effort.  Following is a list of the papers I know about,
which I'm sure is incomplete.  Anyone else working on this topic should
feel free to add to this list!

		Cheers,
				Terry Sanger

@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"}

@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"}

@article{sang89d,
	author="Terence David Sanger",
	title="Analysis of the Two-Dimensional Receptive Fields Learned 
		by the Generalized {Hebbian} Algorithm in Response to 
		Random Input",
	year=1990,
	journal="Biological Cybernetics",
	volume=63,
	pages="221--228"}

@misc{sang90c,
	author="Terence D. Sanger",
	title="Optimal Hidden Units for Two-layer Nonlinear
               Feedforward Neural Networks",
	year=1991,
	note="{\it Int. J. Pattern Recognition and AI}, in press"}

@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}

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

@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{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"}

@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"}

@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"}

@article{leen91,
  author = "Todd K Leen",
  title = "Dynamics of learning in linear feature-discovery networks",
  journal = "Network",
  volume = 2,
  year = "1991",
  pages = "85--105"}

@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"}