On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering.

The strict Cauchy-Riemann-Fueter (CRF) analyticity conditions establish that only linear quaternion-valued functions are analytic, prohibiting the development of quaternion-valued nonlinear adaptive filters for the recurrent neural network architecture (RNN). In this work, the requirement of local...

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Main Authors: Che Ujang, Bukhari, Took, Clive Cheong, Mandic, Danilo P.
格式: Conference or Workshop Item
语言:English
English
出版: 2012
在线阅读:http://psasir.upm.edu.my/id/eprint/31822/1/31822.pdf
http://psasir.upm.edu.my/id/eprint/31822/
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总结:The strict Cauchy-Riemann-Fueter (CRF) analyticity conditions establish that only linear quaternion-valued functions are analytic, prohibiting the development of quaternion-valued nonlinear adaptive filters for the recurrent neural network architecture (RNN). In this work, the requirement of local analyticity in gradient based learning is exercised and proposes to use the local analyticity condition (LAC) to introduce quaternion-valued nonlinear feedback adaptive filters. The introduced class of algorithms make full use of quaternion algebra and provide generic extensions of the corresponding real and complex solutions. Simulations in the prediction setting support the analysis presented.