Title: Model-Independent Analytic Nonlinear Blind Source Separation,
Abstract: 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 perform
nonlinear blind source separation; i.e., how to determine if these signals are
equal to linear or nonlinear mixtures of the state variables of two or more
statistically independent subsystems. First, the local distributions of
measurement velocities are processed in order to derive vectors at each point
in x-space. If the data are separable, each of these vectors must be directed
along a subspace of x-space that is traversed by varying the state variable of
one subsystem, while all other subsystems are kept constant. Because of this
property, these vectors can be used to construct a small set of mappings, which
must contain the unmixing function, if it exists. Therefore, nonlinear blind
source separation can be performed by examining the separability of the data
after it has been transformed by each of these mappings. The method is
analytic, constructive, and model-independent. It is illustrated by blindly
recovering the separate utterances of two speakers from nonlinear combinations
of their audio waveforms.