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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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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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