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

Article

Quaternionic Multilayer Perceptron with Local Analyticity

Teijiro Isokawa ^1,* , Haruhiko Nishimura ²  and Nobuyuki Matsui ¹

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; in revised form: 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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Abstract: 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

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