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# Kurtosis Approach to Solution of a Nonlinear ICA Problem

- Thursday, 02 July 2009

### 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.

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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