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Analysis of the Kurtosis-Sum Objective Function for ICA

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Advances in Neural Networks - ISNN 2008 (ISNN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5263))

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Abstract

The majority of existing Independent Component Analysis (ICA) algorithms are based on maximizing or minimizing a certain objective function with the help of gradient learning methods. However, it is rather difficult to prove whether there is no spurious solution in ICA under any objective function as well as the gradient learning algorithm to optimize it. In this paper, we present an analysis on the kurtosis-sum objective function, i.e., the sum of the absolute kurtosis values of all the estimated components, with a kurtosis switching algorithm to maximize it. In two-source case, it is proved that any local maximum of this kurtosis-sum objective function corresponds to a feasible solution of the ICA problem in the asymptotic sense. The simulation results further show that the kurtosis switching algorithm always leads to a feasible solution of the ICA problem for various types of sources.

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References

  1. Comon, P.: Independent Component Analysis – a New Concept? Signal Processing 36, 287–314 (1994)

    Article  MATH  Google Scholar 

  2. Cardoso, J.F.: Infomax and Maximum Likelihood for Blind Source Separation. IEEE Signal Processing Letters 4, 112–114 (1997)

    Article  Google Scholar 

  3. Bell, A., Sejnowski, T.: An Information-Maximization Approach to Blind Separation and Blind Deconvolution. Neural Computation 7, 1129–1159 (1995)

    Article  Google Scholar 

  4. Amari, S.I., Cichocki, A., Yang, H.: A New Learning Algorithm for Blind Separation of Sources. Advances in Neural Information Processing 8, 757–763 (1996)

    Google Scholar 

  5. Xu, L., Cheung, C.C., Amari, S.I.: Learned Parametric Mixture Based ICA Algorithm. Neurocomputing 22, 69–80 (1998)

    Article  MATH  Google Scholar 

  6. Liu, Z.Y., Chiu, K.C., Xu, L.: One-Bit-Matching Conjecture for Independent Component Analysis. Neural Computation 16, 383–399 (2004)

    Article  MATH  Google Scholar 

  7. Ma, J., Liu, Z.Y., Xu, L.: A Further Result on the ICA One-Bit-Matching Conjecture. Neural Computation 17, 331–334 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ma, J., Chen, Z., Amari, S.I.: Analysis of Feasible Solutions of the ICA Problem under the One-Bit-Matching Condition. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 838–845. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Ma, J., Gao, D., Ge, F., Amari, S.: A One-Bit-Matching Learning Algorithm for Independent Component Analysis. In: Rosca, J.P., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds.) ICA 2006. LNCS, vol. 3889, pp. 173–180. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Vrins, F., Verleysen, M.: Information Theoretic Versus Cumulant-based Contrasts for Multimodal Source Separation. IEEE Signal Processing Letters 12, 190–193 (2005)

    Article  Google Scholar 

  11. Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources. Neural Computation 11, 417–441 (1999)

    Article  Google Scholar 

  12. Zhang, L., Cichocki, A., Amari, S.I.: Self-Adaptive Blind Source Separation Based on Activation Function Adaptation. IEEE Trans. Neural Networks 15, 233–243 (2004)

    Article  Google Scholar 

  13. Ma, J., Ge, F., Gao, D.: Two Aadaptive Matching Learning Algorithms for Indepenedent Component Analysis. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3801, pp. 915–920. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Welling, M., Weber, M.: A Constrained EM Algorithm for Independent Component Analysis. Neural Computation 13, 677–689 (2001)

    Article  MATH  Google Scholar 

  15. Boscolo, R., Pan, H., Roychowdhury, V.P.: Independent Component Analysis Based on Nonparametric Density Estimation. IEEE Trans. Neural Networks 15, 55–64 (2004)

    Article  Google Scholar 

  16. Amari, S.I., Chen, T.P., Cichocki, A.: Stability Analysis of Learning Algorithms for Blind Source Separation. Neural Networks 10, 1345–1351 (1997)

    Article  Google Scholar 

  17. Cardoso, J.F., Laheld, B.: Equivariant Adaptive Source Separation. IEEE Trans. Signal Processing 44, 3017–3030 (1996)

    Article  Google Scholar 

  18. Delfosse, N., Loubaton, P.: Adaptive Blind Separation of Independent Sources: a Deflation Approach. Signal Processing 45, 59–83 (1995)

    Article  MATH  Google Scholar 

  19. Hyvärinen, A., Oja, E.: A Fast Fixed-point Algorithm for Independent Component Analysis. Neural Computation 9, 1483–1492 (1997)

    Article  Google Scholar 

  20. Hyvärinen, A.: Fast and Robust Fixed-point Algorithms for Independent Component Analysis. IEEE Trans. Neural Networks 10, 626–634 (1999)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information Science, School of Mathematical Sciences and LMAM, Peking University, Beijing, 100871, China

    Fei Ge & Jinwen Ma

Authors
  1. Fei Ge
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  2. Jinwen Ma
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghu University, 100084, Beijing, China

    Fuchun Sun

  2. Institute TAMS (Technical Aspects of Multimodal Systems), department of Informatics, University of Hamburg, Vogt-Koelln-Straße 30, 22527, Hamburg, Germany

    Jianwei Zhang

  3. Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence, 100871, Beijing, China

    Ying Tan

  4. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Jinde Cao

  5. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

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© 2008 Springer-Verlag Berlin Heidelberg

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Ge, F., Ma, J. (2008). Analysis of the Kurtosis-Sum Objective Function for ICA. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_65

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  • DOI: https://doi.org/10.1007/978-3-540-87732-5_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87731-8

  • Online ISBN: 978-3-540-87732-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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