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Quaternionic Multilayer Perceptron with Local Analyticity
Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan
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
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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Isokawa, T.; Nishimura, H.; Matsui, N. Quaternionic Multilayer Perceptron with Local Analyticity. Information 2012, 3, 756-770.
Isokawa T, Nishimura H, Matsui N. Quaternionic Multilayer Perceptron with Local Analyticity. Information. 2012; 3(4):756-770.
Isokawa, Teijiro; Nishimura, Haruhiko; Matsui, Nobuyuki. 2012. "Quaternionic Multilayer Perceptron with Local Analyticity." Information 3, no. 4: 756-770.