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Complex-valued ICA based on a pair of generalized covariance matrices

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  • Ollila, Esa
  • Oja, Hannu
  • Koivunen, Visa

Abstract

It is shown that any pair of scatter and spatial scatter matrices yields an estimator of the separating matrix for complex-valued independent component analysis (ICA). Scatter (resp. spatial scatter) matrix is a generalized covariance matrix in the sense that it is a positive definite hermitian matrix functional that satisfies the same affine (resp. unitary) equivariance property as does the covariance matrix and possesses an additional IC-property, namely, it reduces to a diagonal matrix at distributions with independent marginals. Scatter matrix is used to decorrelate the data and the eigenvalue decomposition of the spatial scatter matrix is used to find the unitary mixing matrix of the uncorrelated data. The method is a generalization of the FOBI algorithm, where a conventional covariance matrix and a certain fourth-order moment matrix take the place of the scatter and spatial scatter matrices, respectively. Emphasis is put on estimators employing robust scatter and spatial scatter matrices. The proposed approach is one among the computationally most attractive ones, and a new efficient algorithm that avoids decorrelation of the data is also proposed. Moreover, the method does not rely upon the commonly made assumption of complex circularity of the sources. Simulations and examples are used to confirm the reliable performance of our method.

Suggested Citation

  • Ollila, Esa & Oja, Hannu & Koivunen, Visa, 2008. "Complex-valued ICA based on a pair of generalized covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3789-3805, March.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3789-3805
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    References listed on IDEAS

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    1. Taskinen, S. & Sirkia, S. & Oja, H., 2007. "Independent component analysis based on symmetrised scatter matrices," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5103-5111, June.
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    Cited by:

    1. Navarro-Moreno, Jesús & Moreno-Kaiser, Javier & Fernández-Alcalá, Rosa María & Ruiz-Molina, Juan Carlos, 2013. "Widely linear prediction for transfer function models based on the infinite past," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 139-146.
    2. Lietzén, Niko & Nordhausen, Klaus & Ilmonen, Pauliina, 2016. "Minimum distance index for complex valued ICA," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 100-106.
    3. Ilmonen, Pauliina, 2013. "On asymptotic properties of the scatter matrix based estimates for complex valued independent component analysis," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1219-1226.
    4. Lee, Seonjoo & Shen, Haipeng & Truong, Young, 2021. "Sampling properties of color Independent Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 181(C).

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