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Information 2012, 3(4), 756-770; doi:10.3390/info3040756

Quaternionic Multilayer Perceptron with Local Analyticity

1,* , 2
1 Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan 2 Graduate School of Applied Informatics, University of Hyogo, 7-1-28 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
* Author to whom correspondence should be addressed.
Received: 11 September 2012 / Revised: 13 November 2012 / Accepted: 20 November 2012 / Published: 28 November 2012
(This article belongs to the Special Issue Brain like Computing, Communication and Machines)
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A multi-layered perceptron type neural network is presented and analyzed in this paper. All neuronal parameters such as input, output, action potential and connection weight are encoded by quaternions, which are a class of hypercomplex number system. Local analytic condition is imposed on the activation function in updating neurons’ states in order to construct learning algorithm for this network. An error back-propagation algorithm is introduced for modifying the connection weights of the network.
Keywords: quaternion; local analyticity; Wirtinger calculus; multilayer perceptron; error back-propagation quaternion; local analyticity; Wirtinger calculus; multilayer perceptron; error back-propagation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Isokawa, T.; Nishimura, H.; Matsui, N. Quaternionic Multilayer Perceptron with Local Analyticity. Information 2012, 3, 756-770.

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