Uniqueness of complex and multidimensional independent component analysis

F. J. Theis

doi:10.1016/j.sigpro.2004.01.008

Uniqueness of complex and multidimensional independent component analysis

F. J. Theis

University of Regensburg

Research output: Contribution to journal › Article › peer-review

51 Scopus citations

Abstract

A complex version of the Darmois-Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois-Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.

Original language	English
Pages (from-to)	951-956
Number of pages	6
Journal	Signal Processing
Volume	84
Issue number	5
DOIs	https://doi.org/10.1016/j.sigpro.2004.01.008
State	Published - May 2004
Externally published	Yes

Keywords

Complex ICA
Multidimensional ICA
Separability

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10.1016/j.sigpro.2004.01.008

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title = "Uniqueness of complex and multidimensional independent component analysis",

abstract = "A complex version of the Darmois-Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois-Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.",

keywords = "Complex ICA, Multidimensional ICA, Separability",

author = "Theis, {F. J.}",

note = "Funding Information: This research was supported by Grants from the DFG 2 ",

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N2 - A complex version of the Darmois-Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois-Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.

AB - A complex version of the Darmois-Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois-Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.

KW - Complex ICA

KW - Multidimensional ICA

KW - Separability

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VL - 84

SP - 951

EP - 956

JO - Signal Processing

JF - Signal Processing

IS - 5

ER -

Uniqueness of complex and multidimensional independent component analysis

Abstract

Keywords

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