Information-theoretic approach to blind separation of sources in non-linear mixture
Signal Processing - Special issue on neural networks
Using state space differential geometry for nonlinear blind source separation
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Performing nonlinear blind source separation with signal invariants
IEEE Transactions on Signal Processing
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Given a time series of multicomponent measurements x (t ), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s (t ), comprised of statistically independent combinations of the measured components. In this paper, the source time series is required to have a density function in $(s,\dot{s})$-space that is equal to the product of density functions of individual components. This formulation of the BSS problem has a solution that is unique, up to permutations and component-wise transformations. Separability is shown to impose constraints on certain locally invariant (scalar) functions of x , which are derived from local higher-order correlations of the data's velocity $\dot{x}$. The data are separable if and only if they satisfy these constraints, and, if the constraints are satisfied, the sources can be explicitly constructed from the data. The method is illustrated by using it to separate two speech-like sounds recorded with a single microphone.