2009

Kurtosis Approach to Solution of a Nonlinear ICA Problem

A gradient-descent algorithm minimizes the kurtosis of an output vector.

An algorithm for solving a particular nonlinear independent-component-analysis (ICA) problem, that differs from prior algorithms for solving the same problem, has been devised. The problem in question — of a type known in the art as a post nonlinear mixing problem — is a useful approximation of the problem posed by the mixing and subsequent nonlinear distortion of sensory signals that occur in diverse scientific and engineering instrumentation systems.

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Mixing and Distortion Operations and their inverses are represented in these block-diagram representations of mixing and unmixing models.
Prerequisite for describing this particular post nonlinear ICA problem is a description of the post nonlinear mixing and unmixing models depicted schematically in the figure. The mixing model consists of a linear mixing part followed by a memoryless invertible nonlinear transfer part. The unmixing model consists of a nonlinear inverse transfer part followed by a linear unmixing part. The source signals are recovered if each operation in the unmixing sequence is the inverse of the corresponding operation in the mixing sequence.

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