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A semiparametric approach to source separation using independent component analysis

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  • Eloyan, Ani
  • Ghosh, Sujit K.

Abstract

Data processing and source identification using lower dimensional hidden structure plays an essential role in many fields of applications, including image processing, neural networks, genome studies, signal processing and other areas where large datasets are often encountered. One of the common methods for source separation using lower dimensional structure involves the use of Independent Component Analysis, which is based on a linear representation of the observed data in terms of independent hidden sources. The problem thus involves the estimation of the linear mixing matrix and the densities of the independent hidden sources. However, the solution to the problem depends on the identifiability of the sources. This paper first presents a set of sufficient conditions to establish the identifiability of the sources and the mixing matrix using moment restrictions of the hidden source variables. Under such sufficient conditions a semi-parametric maximum likelihood estimate of the mixing matrix is obtained using a class of mixture distributions. The consistency of our proposed estimate is established under additional regularity conditions. The proposed method is illustrated and compared with existing methods using simulated and real datasets.

Suggested Citation

  • Eloyan, Ani & Ghosh, Sujit K., 2013. "A semiparametric approach to source separation using independent component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 383-396.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:383-396
    DOI: 10.1016/j.csda.2012.09.012
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    References listed on IDEAS

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    1. Dietmar Ferger, 2004. "A continuous mapping theorem for the argmax‐functional in the non‐unique case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 83-96, February.
    2. Ani Eloyan & Sujit Ghosh, 2011. "Smooth density estimation with moment constraints using mixture distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 513-531.
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    Cited by:

    1. Benjamin B. Risk & David S. Matteson & David Ruppert & Ani Eloyan & Brian S. Caffo, 2014. "An evaluation of independent component analyses with an application to resting-state fMRI," Biometrics, The International Biometric Society, vol. 70(1), pages 224-236, March.

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