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

  • Authors:

  • Esa Ollila;Hannu Oja;Visa Koivunen

  • Affiliations:

  • Signal Processing Laboratory, Helsinki University of Technology, P.O. Box 3000, FIN-02015 HUT, Finland;Tampere School of Public Health, University of Tampere, FIN-33014 University of Tampere, Finland;Signal Processing Laboratory, Helsinki University of Technology, P.O. Box 3000, FIN-02015 HUT, Finland

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2008

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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.