Skip to main content
Top

2012 | OriginalPaper | Chapter

Independent Component Analysis

Author : Seungjin Choi

Published in: Handbook of Natural Computing

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Independent component analysis (ICA) is a statistical method, the goal of which is to decompose multivariate data into a linear sum of non-orthogonal basis vectors with coefficients (encoding variables, latent variables, and hidden variables) being statistically independent. ICA generalizes widely used subspace analysis methods such as principal component analysis (PCA) and factor analysis, allowing latent variables to be non-Gaussian and basis vectors to be non-orthogonal in general. ICA is a density-estimation method where a linear model is learned such that the probability distribution of the observed data is best captured, while factor analysis aims at best modeling the covariance structure of the observed data. We begin with a fundamental theory and present various principles and algorithms for ICA.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
go back to reference Amari S, Cardoso JF (1997) Blind source separation: semiparametric statistical approach. IEEE Trans Signal Process 45:2692–2700CrossRef Amari S, Cardoso JF (1997) Blind source separation: semiparametric statistical approach. IEEE Trans Signal Process 45:2692–2700CrossRef
go back to reference Amari S, Chen TP, Cichocki A (1997) Stability analysis of learning algorithms for blind source separation. Neural Networks 10(8):1345–1351CrossRef Amari S, Chen TP, Cichocki A (1997) Stability analysis of learning algorithms for blind source separation. Neural Networks 10(8):1345–1351CrossRef
go back to reference Amari S, Cichocki A (1998) Adaptive blind signal processing – neural network approaches. Proc IEEE (Special Issue on Blind Identification and Estimation) 86(10):2026–2048 Amari S, Cichocki A (1998) Adaptive blind signal processing – neural network approaches. Proc IEEE (Special Issue on Blind Identification and Estimation) 86(10):2026–2048
go back to reference Amari S, Cichocki A, Yang HH (1996) A new learning algorithm for blind signal separation. In: Touretzky DS, Mozer MC, Hasselmo ME (eds) Advances in neural information processing systems (NIPS), vol 8. MIT Press, Cambridge, pp 757–763 Amari S, Cichocki A, Yang HH (1996) A new learning algorithm for blind signal separation. In: Touretzky DS, Mozer MC, Hasselmo ME (eds) Advances in neural information processing systems (NIPS), vol 8. MIT Press, Cambridge, pp 757–763
go back to reference Bach FR, Jordan MI (2003) Beyond independent components: trees and clusters. JMLR 4:1205–1233MathSciNet Bach FR, Jordan MI (2003) Beyond independent components: trees and clusters. JMLR 4:1205–1233MathSciNet
go back to reference Bell A, Sejnowski T (1995) An information maximisation approach to blind separation and blind deconvolution. Neural Comput 7:1129–1159CrossRef Bell A, Sejnowski T (1995) An information maximisation approach to blind separation and blind deconvolution. Neural Comput 7:1129–1159CrossRef
go back to reference Belouchrani A, Abed‐Merain K, Cardoso JF, Moulines E (1997) A blind source separation technique using second order statistics. IEEE Trans Signal Process 45:434–444CrossRef Belouchrani A, Abed‐Merain K, Cardoso JF, Moulines E (1997) A blind source separation technique using second order statistics. IEEE Trans Signal Process 45:434–444CrossRef
go back to reference Cardoso JF (1989) Source separation using higher‐order moments. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), Paris, France, 23–26 May 1989 Cardoso JF (1989) Source separation using higher‐order moments. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), Paris, France, 23–26 May 1989
go back to reference Cardoso JF (1997) Infomax and maximum likelihood for source separation. IEEE Signal Process Lett 4(4):112–114CrossRef Cardoso JF (1997) Infomax and maximum likelihood for source separation. IEEE Signal Process Lett 4(4):112–114CrossRef
go back to reference Cardoso JF, Laheld BH (1996) Equivariant adaptive source separation. IEEE Trans Signal Process 44(12):3017–3030CrossRef Cardoso JF, Laheld BH (1996) Equivariant adaptive source separation. IEEE Trans Signal Process 44(12):3017–3030CrossRef
go back to reference Cardoso JF, Souloumiac A (1993) Blind beamforming for non Gaussian signals. IEE Proc‐F 140(6):362–370 Cardoso JF, Souloumiac A (1993) Blind beamforming for non Gaussian signals. IEE Proc‐F 140(6):362–370
go back to reference Chang C, Ding Z, Yau SF, Chan FHY (2000) A matrix‐pencil approach to blind separation of colored nonstationary signals. IEEE Trans Signal Process 48(3):900–907CrossRef Chang C, Ding Z, Yau SF, Chan FHY (2000) A matrix‐pencil approach to blind separation of colored nonstationary signals. IEEE Trans Signal Process 48(3):900–907CrossRef
go back to reference Choi S (2002) Adaptive differential decorrelation: a natural gradient algorithm. In: Proceedings of the international conference on artificial neural networks (ICANN), Madrid, Spain. Lecture notes in computer science, vol 2415. Springer, Berlin, pp 1168–1173 Choi S (2002) Adaptive differential decorrelation: a natural gradient algorithm. In: Proceedings of the international conference on artificial neural networks (ICANN), Madrid, Spain. Lecture notes in computer science, vol 2415. Springer, Berlin, pp 1168–1173
go back to reference Choi S (2003) Differential learning and random walk model. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), IEEE, Hong Kong, pp 724–727 Choi S (2003) Differential learning and random walk model. In: Proceedings of the IEEE international conference on acoustics, speech, and signal processing (ICASSP), IEEE, Hong Kong, pp 724–727
go back to reference Choi S, Cichocki A (2000a) Blind separation of nonstationary and temporally correlated sources from noisy mixtures. In: Proceedings of IEEE workshop on neural networks for signal processing, IEEE, Sydney, Australia. pp 405–414 Choi S, Cichocki A (2000a) Blind separation of nonstationary and temporally correlated sources from noisy mixtures. In: Proceedings of IEEE workshop on neural networks for signal processing, IEEE, Sydney, Australia. pp 405–414
go back to reference Choi S, Cichocki A (2000b) Blind separation of nonstationary sources in noisy mixtures. Electron Lett 36(9):848–849CrossRef Choi S, Cichocki A (2000b) Blind separation of nonstationary sources in noisy mixtures. Electron Lett 36(9):848–849CrossRef
go back to reference Choi S, Cichocki A, Amari S (2000) Flexible independent component analysis. J VLSI Signal Process 26(1/2):25–38MATHCrossRef Choi S, Cichocki A, Amari S (2000) Flexible independent component analysis. J VLSI Signal Process 26(1/2):25–38MATHCrossRef
go back to reference Choi S, Cichocki A, Belouchrani A (2002) Second order nonstationary source separation. J VLSI Signal Process 32:93–104MATHCrossRef Choi S, Cichocki A, Belouchrani A (2002) Second order nonstationary source separation. J VLSI Signal Process 32:93–104MATHCrossRef
go back to reference Choi S, Cichocki A, Park HM, Lee SY (2005) Blind source separation and independent component analysis: a review. Neural Inf Process Lett Rev 6(1): 1–57 Choi S, Cichocki A, Park HM, Lee SY (2005) Blind source separation and independent component analysis: a review. Neural Inf Process Lett Rev 6(1): 1–57
go back to reference Cichocki A, Amari S (2002) Adaptive blind signal and image processing: learning algorithms and applications. Wiley, ChichesterCrossRef Cichocki A, Amari S (2002) Adaptive blind signal and image processing: learning algorithms and applications. Wiley, ChichesterCrossRef
go back to reference Cichocki A, Unbehauen R (1996) Robust neural networks with on‐line learning for blind identification and blind separation of sources. IEEE Trans Circ Syst Fund Theor Appl 43:894–906CrossRef Cichocki A, Unbehauen R (1996) Robust neural networks with on‐line learning for blind identification and blind separation of sources. IEEE Trans Circ Syst Fund Theor Appl 43:894–906CrossRef
go back to reference Comon P (1994) Independent component analysis, a new concept? Signal Process 36(3):287–314MATHCrossRef Comon P (1994) Independent component analysis, a new concept? Signal Process 36(3):287–314MATHCrossRef
go back to reference Fukunaga K (1990) An introduction to statistical pattern recognition. Academic, New York Fukunaga K (1990) An introduction to statistical pattern recognition. Academic, New York
go back to reference Golub GH, Loan CFV (1993) Matrix computations, 2nd edn. Johns Hopkins, Baltimore Golub GH, Loan CFV (1993) Matrix computations, 2nd edn. Johns Hopkins, Baltimore
go back to reference Haykin S (2000) Unsupervised adaptive filtering: blind source separation. Prentice‐Hall Haykin S (2000) Unsupervised adaptive filtering: blind source separation. Prentice‐Hall
go back to reference Hyvärinen A (1999) Survey on independent component analysis. Neural Comput Surv 2:94–128 Hyvärinen A (1999) Survey on independent component analysis. Neural Comput Surv 2:94–128
go back to reference Hyvärinen A, Hoyer P (2000) Emergence of phase‐ and shift‐invariant features by decomposition of natural images into independent feature subspaces. Neural Comput 12(7):1705–1720CrossRef Hyvärinen A, Hoyer P (2000) Emergence of phase‐ and shift‐invariant features by decomposition of natural images into independent feature subspaces. Neural Comput 12(7):1705–1720CrossRef
go back to reference Hyvärinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New YorkCrossRef Hyvärinen A, Karhunen J, Oja E (2001) Independent component analysis. Wiley, New YorkCrossRef
go back to reference Hyvärinen A, Oja E (1997) A fast fixed‐point algorithm for independent component analysis. Neural Comput 9:1483–1492CrossRef Hyvärinen A, Oja E (1997) A fast fixed‐point algorithm for independent component analysis. Neural Comput 9:1483–1492CrossRef
go back to reference Jutten C, Herault J (1991) Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture. Signal Process 24:1–10MATHCrossRef Jutten C, Herault J (1991) Blind separation of sources, part I: an adaptive algorithm based on neuromimetic architecture. Signal Process 24:1–10MATHCrossRef
go back to reference Karhunen J (1996) Neural approaches to independent component analysis and source separation. In: Proceedings of the European symposium on artificial neural networks (ESANN), Bruges, Belgium, pp 249–266 Karhunen J (1996) Neural approaches to independent component analysis and source separation. In: Proceedings of the European symposium on artificial neural networks (ESANN), Bruges, Belgium, pp 249–266
go back to reference Kim S, Choi S (2005) Independent arrays or independent time courses for gene expression data. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS), Kobe, Japan, 23–26 May 2005 Kim S, Choi S (2005) Independent arrays or independent time courses for gene expression data. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS), Kobe, Japan, 23–26 May 2005
go back to reference Kosko B (1986) Differential Hebbian learning. In: Proceedings of American Institute of Physics: neural networks for computing, Snowbird. American Institute of Physics, Woodbury, pp 277–282 Kosko B (1986) Differential Hebbian learning. In: Proceedings of American Institute of Physics: neural networks for computing, Snowbird. American Institute of Physics, Woodbury, pp 277–282
go back to reference Lee TW (1998) Independent component analysis: theory and applications. KluwerMATH Lee TW (1998) Independent component analysis: theory and applications. KluwerMATH
go back to reference Lee TW, Girolami M, Sejnowski T (1999) Independent component analysis using an extended infomax algorithm for mixed sub‐Gaussian and super‐Gaussian sources. Neural Comput 11(2):609–633CrossRef Lee TW, Girolami M, Sejnowski T (1999) Independent component analysis using an extended infomax algorithm for mixed sub‐Gaussian and super‐Gaussian sources. Neural Comput 11(2):609–633CrossRef
go back to reference Lewicki MS, Sejnowski T (2000) Learning overcomplete representation. Neural Comput 12(2):337–365CrossRef Lewicki MS, Sejnowski T (2000) Learning overcomplete representation. Neural Comput 12(2):337–365CrossRef
go back to reference Li Y, Cichocki A, Amari S (2006) Blind estimation of channel parameters and source components for EEG signals: a sparse factorization approach. IEEE Trans Neural Networ 17(2):419–431CrossRef Li Y, Cichocki A, Amari S (2006) Blind estimation of channel parameters and source components for EEG signals: a sparse factorization approach. IEEE Trans Neural Networ 17(2):419–431CrossRef
go back to reference Liebermeister W (2002) Linear modes of gene expression determined by independent component analysis. Bioinformatics 18(1):51–60CrossRef Liebermeister W (2002) Linear modes of gene expression determined by independent component analysis. Bioinformatics 18(1):51–60CrossRef
go back to reference MacKay DJC (1996) Maximum likelihood and covariant algorithms for independent component analysis. Technical Report Draft 3.7, University of Cambridge, Cavendish Laboratory MacKay DJC (1996) Maximum likelihood and covariant algorithms for independent component analysis. Technical Report Draft 3.7, University of Cambridge, Cavendish Laboratory
go back to reference Matsuoka K, Ohya M, Kawamoto M (1995) A neural net for blind separation of nonstationary signals. Neural Networks 8(3):411–419CrossRef Matsuoka K, Ohya M, Kawamoto M (1995) A neural net for blind separation of nonstationary signals. Neural Networks 8(3):411–419CrossRef
go back to reference Miskin JW, MacKay DJC (2001) Ensemble learning for blind source separation. In: Roberts S, Everson R (eds) Independent component analysis: principles and practice. Cambridge University Press, Cambridge, UK, pp 209–233 Miskin JW, MacKay DJC (2001) Ensemble learning for blind source separation. In: Roberts S, Everson R (eds) Independent component analysis: principles and practice. Cambridge University Press, Cambridge, UK, pp 209–233
go back to reference Molgedey L, Schuster HG (1994) Separation of a mixture of independent signals using time delayed correlations. Phys Rev Lett 72:3634–3637CrossRef Molgedey L, Schuster HG (1994) Separation of a mixture of independent signals using time delayed correlations. Phys Rev Lett 72:3634–3637CrossRef
go back to reference Oja E (1995) The nonlinear PCA learning rule and signal separation – mathematical analysis. Technical Report A26, Helsinki University of Technology, Laboratory of Computer and Information Science Oja E (1995) The nonlinear PCA learning rule and signal separation – mathematical analysis. Technical Report A26, Helsinki University of Technology, Laboratory of Computer and Information Science
go back to reference Pearlmutter B, Parra L (1997) Maximum likelihood blind source separation: a context‐sensitive generalization of ICA. In: Mozer MC, Jordan MI, Petsche T (eds) Advances in neural information processing systems (NIPS), vol 9. MIT Press, Cambridge, pp 613–619 Pearlmutter B, Parra L (1997) Maximum likelihood blind source separation: a context‐sensitive generalization of ICA. In: Mozer MC, Jordan MI, Petsche T (eds) Advances in neural information processing systems (NIPS), vol 9. MIT Press, Cambridge, pp 613–619
go back to reference Pham DT (1996) Blind separation of instantaneous mixtures of sources via an independent component analysis. IEEE Trans Signal Process 44(11): 2768–2779CrossRef Pham DT (1996) Blind separation of instantaneous mixtures of sources via an independent component analysis. IEEE Trans Signal Process 44(11): 2768–2779CrossRef
go back to reference Plumbley MD (2003) Algorithms for nonnegative independent component analysis. IEEE Trans Neural Network 14(3):534–543CrossRef Plumbley MD (2003) Algorithms for nonnegative independent component analysis. IEEE Trans Neural Network 14(3):534–543CrossRef
go back to reference Stone JV (2004) Independent component analysis: a tutorial introduction. MIT Press, Cambridge Stone JV (2004) Independent component analysis: a tutorial introduction. MIT Press, Cambridge
go back to reference Stone JV, Porrill J, Porter NR, Wilkinson IW (2002) Spatiotemporal independent component analysis of event‐related fMRI data using skewed probability density functions. NeuroImage 15(2):407–421CrossRef Stone JV, Porrill J, Porter NR, Wilkinson IW (2002) Spatiotemporal independent component analysis of event‐related fMRI data using skewed probability density functions. NeuroImage 15(2):407–421CrossRef
go back to reference Tong L, Soon VC, Huang YF, Liu R (1990) AMUSE: a new blind identification algorithm. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS), IEEE, New Orleans, pp 1784–1787 Tong L, Soon VC, Huang YF, Liu R (1990) AMUSE: a new blind identification algorithm. In: Proceedings of the IEEE international symposium on circuits and systems (ISCAS), IEEE, New Orleans, pp 1784–1787
go back to reference Welling M, Weber M (2001) A constrained EM algorithm for independent component analysis. Neural Comput 13:677–689MATHCrossRef Welling M, Weber M (2001) A constrained EM algorithm for independent component analysis. Neural Comput 13:677–689MATHCrossRef
Metadata
Title
Independent Component Analysis
Author
Seungjin Choi
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-540-92910-9_13

Premium Partner