On quaternion analyticity: Enabling quaternion-valued nonlinear adaptive filtering

Che Ujang, B, Cheong Took, C and Mandic, DP (2012) On quaternion analyticity: Enabling quaternion-valued nonlinear adaptive filtering ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. pp. 2117-2120.

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Abstract

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. © 2012 IEEE.

Item Type:	Article
Divisions :	Surrey research (other units)
Authors :	Name Email ORCID Che Ujang, B Cheong Took, C c.cheongtook@surrey.ac.uk Mandic, DP
Date :	2012
DOI :	10.1109/ICASSP.2012.6288329
Depositing User :	Symplectic Elements
Date Deposited :	17 May 2017 12:36
Last Modified :	24 Jan 2020 22:32
URI:	http://epubs.surrey.ac.uk/id/eprint/836030

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