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A Contrast Function for Independent Component Analysis Without Permutation Ambiguity

Abstract : This brief deals with the problem of blind source separation (BSS) via independent component analysis (ICA). We prove that a linear combination of the separator output fourth-order marginal cumulants (kurtoses) is a valid contrast function for ICA under prewhitening if the weights have the same sign as the source kurtoses. If, in addition, the source kurtoses are different and so are the linear combination weights, the contrast eliminates the permutation ambiguity typical to ICA, as the estimated sources are sorted at the separator output according to their kurtosis values in the same order as the weights. If the weights equal the source kurtoses, the contrast is a cumulant matching criterion based on the maximum-likelihood principle. The contrast can be maximized by means of a cost-efficient Jacobi-type pairwise iteration. In the real-valued two-signal case, the asymptotic variance of the resulting Givens angle estimator is determined in closed form, leading to the contrast weights with optimal finite-sample performance. A fully blind solution can be implemented by computing the optimum weights from the initial source estimates obtained by a classical ICA stage. An experimental study validates the features of the proposed technique and shows its superior performance compared to related previous methods.
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Contributor : Vicente Zarzoso <>
Submitted on : Sunday, December 5, 2010 - 4:16:41 PM
Last modification on : Thursday, April 22, 2021 - 3:48:03 PM


  • HAL Id : hal-00543058, version 1



Vicente Zarzoso, Pierre Comon, Ronald Phlypo. A Contrast Function for Independent Component Analysis Without Permutation Ambiguity. IEEE Transactions on Neural Networks, Institute of Electrical and Electronics Engineers, 2010, 21 (5), pp.863-868. ⟨hal-00543058⟩



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