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...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English English |
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2012
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| Online Access: | http://psasir.upm.edu.my/id/eprint/31822/ http://psasir.upm.edu.my/id/eprint/31822/1/31822.pdf |
| _version_ | 1848847054037581824 |
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| author | Che Ujang, Bukhari Took, Clive Cheong Mandic, Danilo P. |
| author_facet | Che Ujang, Bukhari Took, Clive Cheong Mandic, Danilo P. |
| author_sort | Che Ujang, Bukhari |
| building | UPM Institutional Repository |
| collection | Online Access |
| description |
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.
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| first_indexed | 2025-11-15T09:12:30Z |
| format | Conference or Workshop Item |
| id | upm-31822 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:12:30Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-318222014-08-04T08:22:15Z http://psasir.upm.edu.my/id/eprint/31822/ On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. Che Ujang, Bukhari Took, Clive Cheong Mandic, Danilo P. 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 Conference or Workshop Item NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/31822/1/31822.pdf Che Ujang, Bukhari and Took, Clive Cheong and Mandic, Danilo P. (2012) On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. In: IEEE International Conference on Acoustics, Speech and Signal Processing , 25-31 Mar. 2012, Kyoto, Japan . (pp. 2117-2120). 10.1109/ICASSP.2012.6288329 English |
| spellingShingle | Che Ujang, Bukhari Took, Clive Cheong Mandic, Danilo P. On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title | On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title_full | On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title_fullStr | On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title_full_unstemmed | On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title_short | On quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| title_sort | on quaternion analyticity : enabling quaternion-valued nonlinear adaptive filtering. |
| url | http://psasir.upm.edu.my/id/eprint/31822/ http://psasir.upm.edu.my/id/eprint/31822/ http://psasir.upm.edu.my/id/eprint/31822/1/31822.pdf |