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The FastICA algorithm

[This is probably the most widely used algorithm for performing independent component analysis, a variant of factor analysis that is completely identifiable unlike classical methods, and able to perform blind source separation.]

FastICA package for Matlab and other systems

A. Hyvärinen. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 10(3):626-634, 1999.
[The fundamental paper on the FastICA algorithm, which is computationally very efficient yet statistically robust.]

A. Hyvärinen and E. Oja. Independent Component Analysis: Algorithms and Applications. Neural Networks, 13(4-5):411-430, 2000.
html (and Japanese version)  Postscript  gzipped PostScript   pdf
[A tutorial text on ICA in general, and FastICA in particular.]

A. Hyvärinen and E. Oja. A Fast Fixed-Point Algorithm for Independent Component Analysis. Neural Computation, 9(7):1483-1492, 1997. Postscript  gzipped PostScript  pdf.
[Introduced the original, cumulant-based, form of the FastICA algorithm.]

 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. Postscript  gzipped PostScript   pdf. Related TechRep: Postscript  gzipped PostScript. pdf.
[Introduced approximations of differential entropy used in the derivation of the FastICA algorithm in the IEEE Transactions paper above.]

E. Bingham and A. Hyvärinen A fast fixed-point algorithm for independent component analysis of complex-valued signals. Int. J. of Neural Systems, 10(1):1-8, 2000.
Postscript  gzipped PostScript  pdf  Matlab code
[A version of FastICA for complex-valued data.]

A. Hyvärinen.  One-Unit Contrast Functions for Independent Component Analysis: A Statistical Analysis.  In Neural Networks for Signal Processing VII (Proc. IEEE NNSP Workshop '97, Amelia Island, Florida), pp. 388--397, 1997. Postscript  gzipped PostScript  pdf.
[Gives a statistical analysis of the maximum nongaussianity framework used in FastICA and some other ICA algorithms given below.]

A. Hyvärinen. The Fixed-Point Algorithm and Maximum Likelihood Estimation for Independent Component Analysis. Neural Processing Letters, 10(1):1-5, 1999.
Postscript  gzipped PostScript  pdf.
[Shows how the FastICA algorithms can be interpreted as maximum likelihood estimation.]

A. Hyvärinen. Gaussian Moments for Noisy Independent Component Analysis. IEEE Signal Processing Letters, 6(6):145--147, 1999.
Postscript  gzipped PostScript  pdf. -- Longer paper with proofs (Proc. ISCAS'99): pdf.
[Shows how to modify the FastICA algorithm obtain consistent estimators when the data is corrupted by Gaussian noise. Introduces the concept of Gaussian moments.]

A. Hyvärinen and U. Köster. FastISA: A fast fixed-point algorithm for independent subspace analysis. Proc. European Symposium on Artificial Neural Networks, Bruges, Belgium, 2006.
gzipped PostScript  pdf
[An analoguous fixed-point algorithm in the case of components which are not independent but have dependencies in the form of subspaces.]