Consider a time series of measurements of the state of an evolving system,x(t), where x has two or more components. This paper shows how to performnonlinear blind source separation; i.e., how to determine if these signals areequal to linear or nonlinear mixtures of the state variables of two or morestatistically independent subsystems. First, the local distributions ofmeasurement velocities are processed in order to derive vectors at each pointin x-space. If the data are separable, each of these vectors must be directedalong a subspace of x-space that is traversed by varying the state variable ofone subsystem, while all other subsystems are kept constant. Because of thisproperty, these vectors can be used to construct a small set of mappings, whichmust contain the unmixing function, if it exists. Therefore, nonlinear blindsource separation can be performed by examining the separability of the dataafter it has been transformed by each of these mappings. The method isanalytic, constructive, and model-independent. It is illustrated by blindlyrecovering the separate utterances of two speakers from nonlinear combinationsof their audio waveforms.
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